express $\displaystyle 3^{n+2}-3^{n}+10(3^{n-1})$ in the simplest form.
$\displaystyle 3^{n+2}-3^{n}+10(3^{n-1})
\Rightarrow
3^{n}3^{2}-3^{n}+10(3^n3^{-1})$
so
$\displaystyle 9(3^{n})-3^{n}+\frac{10}{3}(3^n)$
now combine like terms
$\displaystyle \frac{34}{3}3^n$