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Simplifying cube root expressions | Algebra I | Khan Academy

Video vocabulary

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

multiplication

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US / ˌmʌltɪplɪˈkeɪʃn /

UK / ˌmʌltəplɪˈkeʃən /

B1
  • noun
  • Increase in the number of something
  • Process of multiplying one number by another

sorry

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US / ˈsɒri /

UK / ˈsɑ:ri /

A1
  • exclamation
  • What you say to admit you were wrong
  • adjecitve
  • Causing others to feel pity; poor
  • Feeling regret or sympathy about wrong thing

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

constant

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US / 'kɒnstənt /

UK / ˈkɑnstənt /

A2
  • adjecitve
  • Happening frequently or without pause
  • noun
  • Thing that happens always or at a regular rate

pop

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US / pɒp /

UK / pɑp /

B2
  • adjecitve
  • Type of music or art popular with many people
  • noun
  • Sweet soda drink
  • verb
  • To cause something to open or burst suddenly
  • To go to or in a place for a brief period of time

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

depend

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US / dɪˈpend /

UK / dɪˈpend /

B1
  • verb
  • Be controlled or determined by (someone/something)

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

switch

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US / swɪtʃ /

UK / swɪtʃ /

A2
  • noun
  • A change or shift from one method to another
  • Thing you move to turn electrical items on or off
  • Thin flexible piece of wood or stick
  • verb
  • To exchange or replace something for another thing

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

commutative

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US / kəˈmju:tətɪv /

UK / ˈkɑmjəˌtetɪv, kəˈmjutətɪv /

A1
  • other
  • (Of a binary operation) Independent of order; as in e.g. a x bb x a

exactly

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US / ɪgˈzæktli /

UK / ɪɡˈzæktli /

A1
  • adverb
  • No more and no less than; precisely

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

new

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US / nju: /

UK / nu, nju /

A1
  • adjecitve
  • Not old, recently born, built or made
  • Being or doing something for the first time
  • Not felt, seen or known previously
  • Having been recently bought or obtained

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

matter

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US / 'mætə(r) /

UK / ˈmætɚ /

A1
  • noun
  • Material all things are made of that fills space
  • Problem or reason for concern
  • verb
  • To be of great importance; to count

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

base

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US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

divided

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US / dɪˈvaɪdɪd /

UK / dɪˈvaɪdɪd /

A2
  • adjecitve
  • Being split in two or more pieces
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

decide

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US / dɪ'saɪd /

UK / dɪˈsaɪd /

A2
  • verb
  • To make a choice or choose after thinking about it
  • To make a legal judgment in court
  • to affect the result of something

rest

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US / rest /

UK / rɛst /

A1
  • noun
  • Time when one relaxes, sleeps, or is inactive
  • State in which there is a lack of motion
  • Part of something remaining after some was used
  • verb
  • To stop working or avoid activity to recover
  • (Of dead person) to lie in a grave
  • To lean, support or place something against
  • To not be tired because you had enough sleep

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

swap

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US / swɒp /

UK / swɑp /

B2
  • noun
  • A trade or exchange of goods without using money
  • verb
  • To exchange goods without spending money; trade

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

change

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US / tʃeɪndʒ /

UK / tʃendʒ /

A1
  • noun
  • Exchange of one set of clothes for another
  • Money in the form of coins instead of paper
  • Money returned after giving too much
  • Act of making or becoming something else
  • verb
  • To exchange one set of clothes for another
  • To exchange one kind of money for another
  • To replace something with another thing
  • To make or become something else
  • To go from one train, bus, etc. and go to another

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

fourth

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US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

expression

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US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

color

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US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

associative

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US / əˈsəʊʃiətɪv /

UK / əˈsoʊʃiətɪv /

B1
  • adjecitve
  • Bringing ideas or events together

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

bunch

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US / bʌntʃ /

UK / bʌntʃ /

B1
  • noun
  • A group of things of the same kind
  • verb
  • To group people or things closely together
  • (Cloth) to gather/be gathered together in folds

notation

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US / nəʊ'teɪʃn /

UK / noˈteʃən /

C2
  • noun
  • Set of written signs are used in music or math

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

yeah

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US / jeə /

UK / ˈjɛə, ˈjæə, jɛ- /

A1
  • exclamation
  • Another way of saying 'yes'

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

essentially

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US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

order

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US / 'ɔ:də(r) /

UK / ˈɔrdɚ /

A1
  • noun
  • Religious or social group, as of nuns
  • Instructions to others to do what you want
  • State in which things are neat and organized
  • What you ask to buy, e.g. food in restaurant
  • Social or political control of an area
  • verb
  • To put things in a sequence, e.g. a, b, c
  • To give instructions to others to do what you want
  • To ask for something you want to buy, e.g. a meal

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

root

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US / ru:t /

UK / rut, rʊt /

A2
  • noun
  • Emotional connection with a place, history etc.
  • The origin or starting place of something
  • A number that is multiplied by itself
  • Part of plant growing underground, as to get water
  • Part of tooth, hair etc. from which the rest grows
  • Base part of a word to which affixes can be added
  • verb
  • To cause a plant to develop or grow roots
  • (Animals) to search for e.g. food in earth
  • To stop someone moving, as through fear

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

sixth

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US / sɪksθ /

UK / sɪksθ /

A1
  • noun
  • 6th

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

cube

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US / kju:b /

UK / kjub /

B2
  • noun
  • Solid object that has six square sides
  • verb
  • To cut food into the shape of small cubes
  • To multiply a number by itself three times

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
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have

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UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
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could

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know

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exponent

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US / ɪkˈspəʊnənt /

UK / ɪkˈsponənt, ˈɛkˌsponənt /

C1
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  • Person who exemplifies an art movement, etc.

part

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A1
  • adjecitve
  • To some degree; half; not fully
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  • To make a line in a person's hair, by using a comb
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group

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A1
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  • Subtitles section
  • Multiply and simplify 5 times the cube root of 2x squared times 3 times the cube root of 4x to the fourth.
  • So the two things that pop out of my brain right here is that we can change the order a little bit because multiplication is both commutative-- well, the commutative property allows us to switch the order for multiplication.
  • And so we can get the constant terms.
  • We can multiply the 5 times the 3.
  • And then the other two things that we're multiplying-- they're both the cube root, which is the same thing as taking something to the 1/3 power.
  • So the cube root of x-- this is exactly the same thing as raising x to the 1/3.
  • So let's do that.
  • Let's switch the order and let's rewrite these cube roots as raising it to the 1/3 power.
  • So I have the 5 and the 3.
  • So that's going to be 5 times 3.
  • And then we have the cube root of-- do that in a new color.
  • Then we have the cube root of 2x squared.
  • So this I can rewrite as 2x squared to the 1/3 power.
  • And then I have the cube root of 4x to the fourth.
  • So that's the same thing as 4x to the fourth to the 1/3 power.
  • And now we know from our exponent properties, if we have two things that are both raised to the same power and then we take their product, we could just take their product first and then raise it to the power.
  • So if I have a to the x power times b to the x power, this is the same thing as a times b to the x power.
  • So we can simplify this part of the expression right over here as 2x squared times 4x to the fourth to the 1/3 power.
  • And of course, 5 times 3 is 15.
  • And if we simplify what's in the expression right over here-- once again, it's commutative, so we can swap the order.
  • And it's associative, and so we can swap the groupings.
  • How we group them doesn't matter because it's all multiplication here.
  • This is 2 times 4, which is 6, times x squared times x to the fourth. x squared times x to the fourth is x to the sixth power.
  • And it's all of that to the 1/3 power.
  • And then that is times that-- oh, sorry.
  • Not 6.
  • 2 times 4 is 8.
  • What am I doing?
  • 2 times 4 is 8.
  • x squared times x to the fourth is x to the sixth.
  • I think my brain was adding the exponents and wrote the 6 down.
  • Of course, 2 times 4 is 8, not 6.
  • But we add the exponents.
  • They have the same base.
  • x squared times x to the fourth is x to the sixth.
  • And we're going to raise that to the 1/3 power.
  • And then all of that is times 15.
  • And then we essentially can use this property again.
  • Actually, not that property.
  • We know that this-- well, actually, yeah, exactly this property again.
  • We have something multiplied to a power.
  • This is the exact same thing.
  • This is the exact same thing as 8 to the 1/3 power times x to the sixth to the 1/3 power.
  • And then all of that is being multiplied by 15.
  • And so 8 to the 1/3 power-- that's the same thing as the cube root of 8.
  • You might recognize that 8 is 2 times 2 times 2.
  • So 8 to the 1/3 power is 2.
  • 8 is 2 to the third.
  • So 2 the third to the 1/3 is 2 to the first.
  • 2 times 2 times 2 is 8.
  • And x to the sixth to the 1/3 we know from our exponent properties.
  • That's the same thing as x to the sixth times 1/3 power, or x to the 6 divided by 3 power.
  • Or 6 divided by 3 is 2, or x squared.
  • So that is just x squared.
  • So you have 15 times 2, which gives us 30.
  • So that's these terms right over here.
  • And then you have this term right over here.
  • I want to do that in a different color.
  • And then you have this term right over-- that's not a different color.
  • You have this term right over here is x squared, and you are done.
  • And there's a bunch of ways you could do it.
  • You might not decide to use exponent notation.
  • You could say, look, this is a cube root.
  • I can then take the cube root of the product of both of them.
  • So you don't have to write a 1/3 here.
  • You could just write the cube root of this whole thing over here.
  • And then, depending on how you want to group it and all the rest, you could do this in different orders.
  • As long as you get the right exponent properties, you should get to this same answer.