Question 285144
If the expression is
{{{root(3, a)*root(5, a)}}}
then these are not square roots. The first one is a 3rd root (aka cube root). It represents whatever you cube to get "a". And the second one is a 5th root (what ever you raise to the 5th power to get "a").<br>
To simplify this expression, you do what it says: "write in exponential form." Any radical can be rewritten using fractional exponents:
{{{sqrt(x) = root(2, x) = x^(1/2)}}}
{{{root(3, x) = x^(1/3)}}}
{{{root(4, x) = x^(1/4)}}}
{{{root(5, x) = x^(1/5)}}}
etc.<br>
Rewriting your radcials with fractional exponents we get:
{{{a^(1/3)*a^(1/5)}}}
And the rule for exponents when multiplying like this is to add the exponents. This gives us:
{{{a^(1/3+1/5)}}}
To add the exponents, which are fractions, we need a common denominator:
{{{a^(5/15+3/15)}}}
{{{a^(8/15)}}}
This may be an acceptable answer. But if you want to rewrite this back in radical form:
{{{(a^8)^(1/15)}}}
{{{root(15, a^8)}}}