Question 389984
{{{root(8, 25a^2b^6)}}}
There are no factors of {{{25a^2b^4}}} that are powers of 8 so we cannot simplify this as it stands. Using a rational exponent for the 8th root we have:
{{{(25a^2b^6)^(1/8)}}}
Since {{{25a^2b^4}}} is a perfect square we can rewrite it as: {{{(5ab^2)^2}}}:
{{{((5ab^2)^2)^(1/8)}}}
The rule for exponents when raising a power to a power is to multiply the exponents:
{{{(5ab^2)^(2*(1/8))}}}
which simplifies to:
{{{(5ab^2)^(1/4)}}}
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(4, 5ab^2)}}}