## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$32$
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. --- Thus, we have: $\lim\limits_{x \to 2} (3x-2)^{5/2}=(\lim\limits_{x \to 2} [(3x-2)^{5/2}]=[(3)(2)-2]^{5/2} =4^{5/2} =(2)^{5}=32$