Answer
$32$
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:
$\lim\limits_{x \to 2} (3x-2)^{5/2}=(\lim\limits_{x \to 2} [(3x-2)^{5/2}]=[(3)(2)-2]^{5/2} =4^{5/2} =(2)^{5}=32$
