Answer
$a)$ $4$
$b)$ $\dfrac{3}{2}$
$c)$ $\dfrac{8}{27}$
Work Step by Step
$a)$ $32^{2/5}$
Rewrite the expression as a radical expression and evaluate:
$32^{2/5}=\sqrt[5]{32^{2}}=\sqrt[5]{1024}=4$
$b)$ $\Big(\dfrac{4}{9}\Big)^{-1/2}$
Switch the numerator and the denominator and change the sign of the exponent:
$\Big(\dfrac{4}{9}\Big)^{-1/2}=\Big(\dfrac{9}{4}\Big)^{1/2}=...$
Rewrite as a radical expression and evaluate:
$...=\sqrt{\dfrac{9}{4}}=\dfrac{3}{2}$
$c)$ $\Big(\dfrac{16}{81}\Big)^{3/4}$
Rewrite this as a radical expression and evaluate:
$\Big(\dfrac{16}{81}\Big)^{3/4}=\sqrt[4]{\Big(\dfrac{16}{81}\Big)^{3}}=\sqrt[4]{\dfrac{4096}{531441}}=\dfrac{8}{27}$
