Answer
$a)$ $\dfrac{1}{2}$
$b)$ $2$
$c)$ $\dfrac{1}{3}$
Work Step by Step
$a)$ $\sqrt[5]{\dfrac{1}{8}}\sqrt[5]{\dfrac{1}{4}}$
Evaluate the product:
$\sqrt[5]{\dfrac{1}{8}}\sqrt[5]{\dfrac{1}{4}}=\sqrt[5]{\dfrac{1}{32}}=...$
Evaluate the fifth root:
$..=\sqrt[5]{\dfrac{1}{32}}=\dfrac{1}{2}$
$b)$ $\sqrt[6]{\dfrac{1}{2}}\sqrt[6]{128}$
Evaluate the product:
$\sqrt[6]{\dfrac{1}{2}}\sqrt[6]{128}=\sqrt[6]{64}=...$
Evaluate the sixth root:
$...=\sqrt[6]{64}=2$
$c)$ $\dfrac{\sqrt[3]{4}}{\sqrt[3]{108}}$
Evaluate the division:
$\dfrac{\sqrt[3]{4}}{\sqrt[3]{108}}=\sqrt[3]{\dfrac{4}{108}}=\sqrt[3]{\dfrac{1}{27}}=...$
Evaluate the cubic root:
$...=\sqrt[3]{\dfrac{1}{27}}=\dfrac{1}{3}$
