SOLUTION: My son asked for help and I am at a loss to explain the steps to simplifying. Please show me the steps in hopes I can explain to him and it will trigger an understanding. Two p

Algebra ->  Radicals -> SOLUTION: My son asked for help and I am at a loss to explain the steps to simplifying. Please show me the steps in hopes I can explain to him and it will trigger an understanding. Two p      Log On


   

Question 809770: My son asked for help and I am at a loss to explain the steps to simplifying. Please show me the steps in hopes I can explain to him and it will trigger an understanding.
Two problems:
Simply Sqrt(2)*cuberoot(2^4)
(Ab^-2)^-1/3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Simply Sqrt(2)*cuberoot(2^4)
I think you meant simplify.
= sqrt%282%29%2Aroot%283%2C2%5E4%29
= 2%5E%281%2F2%29%2A2%5E%284%2F3%29
= 2%5E%2811%2F6%29
----------------
= root%286%2C2048%29
= 2%2Aroot%286%2C32%29
I don't know which is the simplest. It's a nebulous term.
----------------
(Ab^-2)^-1/3
Multiply exponents.
= a%5E%28-1%2F3%29b%5E2%2F3%29
-----------------
= root%283%2C%28b%5E2%2Fa%29%29
= root%283%2C%28a%5E2b%5E2%2Fa%5E3%29%29
= root%283%2C%28a%5E2b%5E2%29%29%2Fa