Answer
16
Work Step by Step
We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this along with the power and root rules for limits, we have
$\lim\limits_{y \to -3}(5-y)^{\frac{4}{3}}=(5-(-3))^{\frac{4}{3}}=(5+3)^{\frac{4}{3}}=(8)^{\frac{4}{3}}=(8^{\frac{1}{3}})^4=2^4=16.$
