Answer
(They ask you to write the answer in your own words.)
You can get $x^{2}$ $\times$ $x^{3}$ = $x^{5}$ by using the exponent product rule . $3$ $+$ $2$ $=$ $5$. Why does this work, though?
$x^{2}$ is $x$ $\times$ $x$.
$x^{3}$ is $x$ $\times$ $x$ $\times$ $x$
So essentially, the problem $x^{2}$ $\times$ $x^{3}$ = $x^{5}$ is $x$ $\times$ $x$ $\times$ $x$ $\times$ $x$ $\times$ $x$.
And that is $x^{5}$.
How would you solve ($x^{2}$)$^{3}$?
Using the exponent power rule, you would multiply $3$ $\times$ $2$ $=$ $6$. And you would get $x^{6}$. But why does this rule work?
($x^{2}$)$^{3}$ is basically $x^{2}$ $\times$ $x^{2}$ $\times$ $x^{2}$
So that is basically $x$ $\times$ $x$ $\times$ $x$ $\times$ $x$ $\times$ $x$ $\times$ $x$
And that equals $x^{6}$.
Work Step by Step
This is an explanation problem so there is no step-by-step work; the answer is above.
