Question 817140
{{{(b^(3/4)/a^(-1/2))^8}}}
To start we can use the {{{(a/b)^n = a^n/b^n}}} rule to raise the fraction to the 8th power:
{{{(b^(3/4))^8/(a^(-1/2))^8}}}
Next we use the {{{(a^n)^m = a^(n*m)}}} rule to raise the powers of a power:
{{{b^((3/4)*8)/a^((-1/2)*8)}}}
Simplifying...
{{{b^6/a^(-4)}}}<br>
Now we will deal with the negative exponent. (Some like to deal with this first. But I prefer to wait until the end. Sometimes the negative exponents disappear on their own while working out the rest of the problem. In those cases it would be been a waste of time to have bothered with them at the start.) Since {{{a^(-n) = 1/a^n}}} our expression becomes:
{{{b^6/(1/a^4)}}}
which simplifies to:
{{{a^4 * b^6}}}