Consider the following given function and given interval.

$g(x)=(x2{)}^3,[0,2]$

$($a$)$ Find the average value $g$ ave of $g$ on the given interval.

$g_{\text{a}\text{v}\text{e}}=\frac{?}{\text{E}\text{n}\text{t}\text{e}\text{r}\text{a}\text{f}\text{r}\text{a}\text{c}\text{t}\text{i}\text{o}\text{n}\text{,}\text{i}\text{n}\text{t}\text{e}\text{g}\text{e}\text{s}\text{,}or\text{e}\text{x}\text{a}\text{c}\text{t}\text{d}\text{e}\text{d}\text{i}\text{m}\text{a}\text{l}\text{.}Do\text{r}\text{o}\text{t}\text{a}\text{p}\text{p}\text{r}\text{e}\text{x}\text{i}\text{m}\text{u}\text{l}\text{e}\text{.}}$

$($b$)$ Find $c$ in the given interval such that $g_{\text{a}\text{v}\text{e}}=g(c).($Enter your answers as a comma$-$separated list. Round your answers to three decimal places.$)$

$c=$

$$