Answer
$32$
Work Step by Step
Recall:
(1) $\lim _{x\rightarrow c}\left( f\left( x\right) \right) ^{n}=\left( \lim _{x\rightarrow c}f\left( x\right) \right) ^{n}$
(2) $\lim _{x\rightarrow c}f(x) = f(c)$
Use the rules above to have:
$\lim _{x\rightarrow 2}\left( 3x-2\right) ^{\frac {5}{2}}
\\=\left( \lim _{x\rightarrow 2}3x-2\right) ^{\frac {5}{2}}
\\=\left( 3\times 2-2\right) ^{\frac {5}{2}}
\\=4^{\frac {5}{2}}
\\=2^{5}
\\=32$
