Question 69022
The cube of x is written {{{(x^3)}}}

Raising this to the 5 power is written as {{{(x^3)^5}}}

Notice that {{{(x^3)^5}}} represents {{{x^3)}}} multiplied by itself 5 times ... or:

{{{x^3}}}*{{{x^3}}}*{{{x^3}}}*{{{x^3}}}*{{{x^3}}}

and we multiply common terms with exponents by adding the exponents to get:

{{{x^3}}}*{{{x^3}}}*{{{x^3}}}*{{{x^3}}}*{{{x^3}}} = {{{x^(3+3+3+3+3)}}}

which simplifies to {{{x^15}}}

The shorthand way of doing this is to use the rule that when a term with an exponent is raised to another exponent, you multiply the two exponents.  In this case:

{{{(x^3)^5}}} 

is found by multiplying the 3 by the 5 to get {{{x^15}}}

Hope this helps you to understand exponents a little more.