Question 374383
{{{3^(5/8)/3^(-1/8)}}}
The rules for exponents are the same <b>all</b> exponents. The fact that there are fractional and/or negative exponents do not change the rules! This is a division involving the same base, 3. The rule here is to subtract the exponents (the numerator's exponent minus the denominator's exponent). Applying this rule to your expression we get:
{{{3^((5/8)-(-1/8))}}}
or
{{{3^((5/8)+(1/8))}}}
Fortunately the two fractions have the same denominator so we can go ahead and add them:
{{{3^(6/8)}}}
The fraction will reduce:
{{{3^(3/4)}}}
This may be an acceptable answer. But we can rewrite this using the fact that {{{a^(p/q) = root(q, a^p)}}}:
{{{root(4, 3^3)}}}
Since {{{3^3 = 27}}} this becomes:
{{{root(4, 27)}}}