Answer
$a)$ $\dfrac{1}{4y^{2}}$
$b)$ $\dfrac{1}{u^{4/3}v^{2}}$
Work Step by Step
$a)$ $(8y^{3})^{-2/3}$
Rewrite this expression as a fraction to change the sign of the exponent:
$(8y^{3})^{-2/3}=\dfrac{1}{(8y^{3})^{2/3}}=...$
Evaluate the power in the denominator and simplify:
$...=\dfrac{1}{(8^{2/3})y^{2}}=\dfrac{1}{(\sqrt[3]{8^{2}})y^{2}}=\dfrac{1}{4y^{2}}$
$b)$ $(u^{4}v^{6})^{-1/3}$
Rewrite this expression as a fraction to change the sign of the exponent:
$(u^{4}v^{6})^{-1/3}=\dfrac{1}{(u^{4}v^{6})^{1/3}}=...$
Evaluate the power and simplify:
$...=\dfrac{1}{u^{4/3}v^{2}}$
