Answer
$a)$ $25$
$b)$ $\dfrac{125}{512}$
$c)$ $\dfrac{1}{81}$
Work Step by Step
$a)$ $125^{2/3}$
Rewrite this as a radical expression and evaluate:
$125^{2/3}=\sqrt[3]{125^{2}}=\sqrt[3]{15625}=25$
$b)$ $\Big(\dfrac{25}{64}\Big)^{3/2}$
Rewrite this as a radical expression and evaluate:
$\Big(\dfrac{25}{64}\Big)^{3/2}=\sqrt{\Big(\dfrac{25}{64}\Big)^{3}}=\Big(\dfrac{25}{64}\Big)\sqrt{\dfrac{25}{64}}=\Big(\dfrac{25}{64}\Big)\Big(\dfrac{5}{8}\Big)=\dfrac{125}{512}$
$c)$ $27^{-4/3}$
Rewrite the expression to change the sign of the exponent:
$27^{-4/3}=\dfrac{1}{27^{4/3}}=...$
Now, rewrite the denominator as a radical expression and evaluate:
$...=\dfrac{1}{\sqrt[3]{27^{4}}}=\dfrac{1}{27\sqrt[3]{27}}=\dfrac{1}{27(3)}=\dfrac{1}{81}$
