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### Course: Algebra (all content) > Unit 11

Lesson 7: Simplifying radicals (higher-index roots)# Simplifying cube root expressions (two variables)

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

## Want to join the conversation?

- what do you do when the whole number is not a perfect cube number?(4 votes)
- you would up with an answer of something like 54.09. it depends on what the question asks you to to do.(6 votes)

- 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.(3 votes) - Why does Sal change it to ³√ to ^⅓?(2 votes)
- It is essentially the same thing.

Sal did it perhaps to show you the relations between the power and the roots.(4 votes)

- What is 3 to the -½ power?(2 votes)
- 0:52why do you factor(2 votes)
- So that we can manipulate all the other variables in an equation to find the value of a missing variable.(3 votes)

- 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?(2 votes)
- 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(2 votes)

- at0:30you 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?(1 vote)
- 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.(3 votes)

- 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 ?(1 vote)
- 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(1 vote)

- 1) Subtract 7/x from both sides: 1/4 = 2/x

2) At this point, you have 2 options. You have a proportion so you can cross multiply. Or, you can use the LCD = 4x and multiply both sides by the LCD. You will get:

x = 8

Hope this helps.(2 votes)

- 11 to the negative 4th power over 11 to the 8th power(1 vote)
- 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)(2 votes)

## 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.