Answer
$-1$
Work Step by Step
In order to simplify the given expression, we will use the following rules:
(a) $\lim\limits_{x \to a} [k(x)]^n =[\lim\limits_{x \to a} k(x)]^n$
(b) $\lim\limits_{x \to a} k(x)=k(a)$
where $a$ is a constant.
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Thus, we have:
$\lim\limits_{x \to -1} (2x+1)^{5/3}=[\lim\limits_{x \to -1} [(2x+1)^{5/3}] \\ =[(2)(-1)+1]^{5/3} \\ =(-1)^{5/3} \\ =-1$
