what do you do when the whole number is not a perfect cube number?

you would up with an answer of something like 54.09. it depends on what the question asks you to to do.

I need to find the topic of powers of powers (exponents) or taking a power to a power, could someone help me find a video where Sal explains that please? Much appreciated.

Try this one: https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-3

0:52 why do you factor

So that we can manipulate all the other variables in an equation to find the value of a missing variable.

I am asked to simplify using laws of exponents and write the final answer in exponential form. What does that mean ? how do i do that?

you will be given an equation or expression with lots of exponents in, that means it has lots of things to the power of other things. when you see two exponents timesed together like 2^3 * 2^4 you may simply add the two exponents giving 2^7. if you send me the question I can explain how to do that particular one

Why does Sal change it to ³√ to ^⅓?

It is essentially the same thing. Sal did it perhaps to show you the relations between the power and the roots.

at 0:30 you write and say that we have to think that the cube root is the same thing as powering a number by 1/3. Do we have to do it or can we just factorize from the cube root?

Well, you can solve something raised to the 1/3 by taking the cube root directly. It's just about understanding the root relationship to fractions as it will become even more important when it becomes things like 2/3, or properties that can't be directly found by taking a root.

11 to the negative 4th power over 11 to the 8th power

When dividing two powers with the same base, you subtract the exponents. So 11^(-4) divided by 11^8 equals 11^(-4-8) -4-8=-12, so the answer is 11^(-12). The answer you're looking for is probably "11 to the negative 12th power," since expanding that would be a very tiny decimal.. approximately 3.1863082 x 10^(-13)

Main content

Algebra (all content)

Course: Algebra (all content) > Unit 11

Lesson 7: Simplifying radicals (higher-index roots)

Simplifying cube root expressions (two variables)

Name: Simplifying cube root expressions (two variables)
Uploaded: 2011-06-23T23:27:43Z
Description: Sal simplifies ∛(125x⁶y³) as 5x²y.

Google Classroom

Sal simplifies ∛(125x⁶y³) as 5x²y. Created by Sal Khan and Monterey Institute for Technology and Education.

Want to join the conversation?

Sort by:

Shannon Marie Lucio
Posted 10 years ago. Direct link to Shannon Marie Lucio's post “what do you do when the w...”
what do you do when the whole number is not a perfect cube number?
Button navigates to signup pageComment on Shannon Marie Lucio's post “what do you do when the w...”
(4 votes)
Answer
- Rahul Arasikere
  Posted 10 years ago. Direct link to Rahul Arasikere's post “you would up with an answ...”
  you would up with an answer of something like 54.09. it depends on what the question asks you to to do.
  Comment on Rahul Arasikere's post “you would up with an answ...”
  (6 votes)
Brisa Chase
Posted 10 years ago. Direct link to Brisa Chase's post “I need to find the topic ...”
I need to find the topic of powers of powers (exponents) or taking a power to a power, could someone help me find a video where Sal explains that please?
Much appreciated.
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Sandy Knight
  Posted 10 years ago. Direct link to Sandy Knight's post “Try this one: https://ww...”
  Try this one:
  
  https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-3
  Button navigates to signup page
  (4 votes)
🤔 ᴄᴏᴅᴇᴅ ɢᴇɴɪᴜȿ 😎
Posted 6 years ago. Direct link to 🤔 ᴄᴏᴅᴇᴅ ɢᴇɴɪᴜȿ 😎's post “Why does Sal change it to...”
Why does Sal change it to ³√ to ^⅓?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Shawn
  Posted 6 years ago. Direct link to Shawn's post “It is essentially the sam...”
  It is essentially the same thing.
  Sal did it perhaps to show you the relations between the power and the roots.
  Comment on Shawn's post “It is essentially the sam...”
  (4 votes)
Francisco R. Acuña
Posted 10 years ago. Direct link to Francisco R. Acuña's post “What is 3 to the -½ power...”
What is 3 to the -½ power?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
Shamarr Voskuil
Posted 10 years ago. Direct link to Shamarr Voskuil's post “0:52 why do you factor”
0:52
why do you factor
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Petrie (Peter S. Asiain III)
  Posted 10 years ago. Direct link to Petrie (Peter S. Asiain III)'s post “So that we can manipulate...”
  So that we can manipulate all the other variables in an equation to find the value of a missing variable.
  Comment on Petrie (Peter S. Asiain III)'s post “So that we can manipulate...”
  (3 votes)
abishek raju
Posted 10 years ago. Direct link to abishek raju's post “I am asked to simplify us...”
I am asked to simplify using laws of exponents and write the final answer in exponential form. What does that mean ? how do i do that?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Max Hatfull
  Posted 10 years ago. Direct link to Max Hatfull's post “you will be given an equa...”
  you will be given an equation or expression with lots of exponents in, that means it has lots of things to the power of other things. when you see two exponents timesed together like 2^3 * 2^4 you may simply add the two exponents giving 2^7. if you send me the question I can explain how to do that particular one
  Comment on Max Hatfull's post “you will be given an equa...”
  (2 votes)
Andrea
Posted 9 years ago. Direct link to Andrea's post “at 0:30 you write and say...”
at
0:30
you write and say that we have to think that the cube root is the same thing as powering a number by 1/3. Do we have to do it or can we just factorize from the cube root?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Barrett Southworth
  Posted 9 years ago. Direct link to Barrett Southworth's post “Well, you can solve somet...”
  Well, you can solve something raised to the 1/3 by taking the cube root directly. It's just about understanding the root relationship to fractions as it will become even more important when it becomes things like 2/3, or properties that can't be directly found by taking a root.
  Button navigates to signup page
  (3 votes)
abdul khalik
Posted 12 years ago. Direct link to abdul khalik's post “what is (33/17) whole the...”
what is (33/17) whole the power of -15 divided by (33/170 whole to the power of 8 = (33/17) whole to the power of 4x-9 find x ?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- karen.duseau
  Posted 12 years ago. Direct link to karen.duseau's post “If you have like bases, y...”
  If you have like bases, you can set your exponents equal. So if((33/17)^-15)/(33/17)^8 =(33/17)^4x-9, THEN (-15/8)=4x-9, so multiply by 8 and -15=32x-72, now add 72 to each side, and -57 = 32x, and -1.78125 = x
  Button navigates to signup page
  (1 vote)
Sylvester Demery
Posted 6 years ago. Direct link to Sylvester Demery's post “11 to the negative 4th po...”
11 to the negative 4th power over 11 to the 8th power
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Katherine Steuber
  Posted 6 years ago. Direct link to Katherine Steuber's post “When dividing two powers ...”
  When dividing two powers with the same base, you subtract the exponents.
  So 11^(-4) divided by 11^8 equals 11^(-4-8)
  -4-8=-12, so the answer is 11^(-12).
  The answer you're looking for is probably "11 to the negative 12th power," since expanding that would be a very tiny decimal.. approximately 3.1863082 x 10^(-13)
  Button navigates to signup page
  (2 votes)
hjhduke
Posted 11 years ago. Direct link to hjhduke's post “I have a further question...”
I have a further question re: karen duseau's answer to abdulkhalik2007's question. Shouldn't you be able to do (33/17)^-15-8 = (33/17)^4x-9 so that you then get -23=4x-9? In that case I get x=-7/2 which is different from your answer. Can anybody explain to my why what I did is wrong (if it is)? thanks.
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Vera.Piero
  Posted 8 years ago. Direct link to Vera.Piero's post “disculpen por interrumpir...”
  disculpen por interrumpir su conversacion pero quiero escribir por primera vez algo en respuesta de khan a las 8/53 en el dia 07/04/2015
  Button navigates to signup page
  (1 vote)

Video transcript

Simplify the cube root of 125 x to the sixth y to the third power. So taking the cube root of something is the same thing as raising that something to the 1/3 power. So this is equal to 125 x to the sixth y to the third power raised to the 1/3 power. And if we take a product of a bunch of stuff and raise that to the 1/3 power, that's the same thing as individually raising each of the things to the 1/3 power and then taking the product. So this is going to be equal to 125 to the 1/3 power times x to the sixth to the 1/3 power times y to the third to the 1/3 power. And then we can think about how we can simplify each of these. What's 125 to the 1/3? Well, let's just factor and see if we can have at least three prime factors of something and maybe more than one prime factor that shows up three times. So 125 is 5 times 25. 25 is 5 times 5. So 125 really is 5 times 5 times 5. So if you multiply 5 times itself three times you get 125. 125 to the 1/3 power is going to be 5. So this is going to simplify to 5 times. And then x to the sixth to the 1/3 power-- we saw this in a previous example-- if you raise a base to an exponent and then raise that whole thing to another exponent, you can take the product of the two exponents. So 6 times 1/3 is 6/3 or 2. So this part right over here simplifies to x to the sixth divided by 3 power or x squared. And then finally over here, same principle. Raising y to the third power, and then that to the 1/3 power. So that's going to be y to the 3 times 1/3 power, or y to the first power. And then times y. And we are done. And if you don't want to write this little multiplication here, you could just write this as 5x squared y. And we have simplified.