Answer
512
Work Step by Step
see: Rules for Limits
Let $a, A$, and $B$ be real numbers,
and let $f$ and $g$ be functions such that
$\displaystyle \lim_{x\rightarrow a}f(x)=A$ and $\displaystyle \lim_{x\rightarrow a}g(x)=B$.
8. For any real number $b>0,$
$\displaystyle \lim_{x\rightarrow a}b^{f(x)}=b^{[\lim_{x\rightarrow a}f(x)]}=b^{A}$.
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$\displaystyle \lim_{x\rightarrow 4}2^{f(x)}=2^{\lim_{x\rightarrow 4}f(x)}$
$=2^{9}$
$=512$
