SOLUTION: 8th root of (25a^2b^6) Use rational exponents to simplify expression. Answer in simplified radical form.

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Question 389984: 8th root of (25a^2b^6) Use rational exponents to simplify expression. Answer in simplified radical form.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
root%288%2C+25a%5E2b%5E6%29
There are no factors of 25a%5E2b%5E4 that are powers of 8 so we cannot simplify this as it stands. Using a rational exponent for the 8th root we have:
%2825a%5E2b%5E6%29%5E%281%2F8%29
Since 25a%5E2b%5E4 is a perfect square we can rewrite it as: %285ab%5E2%29%5E2:
%28%285ab%5E2%29%5E2%29%5E%281%2F8%29
The rule for exponents when raising a power to a power is to multiply the exponents:
%285ab%5E2%29%5E%282%2A%281%2F8%29%29
which simplifies to:
%285ab%5E2%29%5E%281%2F4%29
We have simplified the expression as far as it can be simplified. Since we want the answer to be in radical form we rewrite an exponent as 1/4 as a 4th root:
root%284%2C+5ab%5E2%29