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# Simplifying cube root expressions (two variables)

CCSS.Math:

## 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 x 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 125th what's 125 to the 1/3 well let's just factor it and see if we can have at least three prime factors of something and maybe and maybe more than one prime factor that shows up three times so 21 25 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 3 times you get 125 or 20 125 to the 1/3 power is going to be is going to be 5 so this is going to simplify to 5 times and then X to the 6 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 thirds or 2 so this part right over here simplifies to X to the 6 divided by 3 power or x squared x squared and then finally over here same principle raising Y to the 3rd power and then that to the one third power so that's going to be Y to the 3 times one third 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 can just write this as 5x squared 5x squared 5x squared y and we have simplified