Question

which expression represents ((8m)^{\frac{1}{3}}) in radical form?
a) (2sqrt3{m})
b) (sqrt3{2m})
c) (\frac{8}{3}sqrt3{m})
d) (2m)

Explanation:

Step1: Split the exponent

$(8m)^{\frac{1}{3}} = 8^{\frac{1}{3}} \times m^{\frac{1}{3}}$

Step2: Convert to radical form

$8^{\frac{1}{3}} = \sqrt[3]{8}$, $m^{\frac{1}{3}} = \sqrt[3]{m}$

Step3: Simplify $\sqrt[3]{8}$

$\sqrt[3]{8} = 2$

Step4: Combine terms

$2 \times \sqrt[3]{m} = 2\sqrt[3]{m}$

Answer:

A) $2\sqrt[3]{m}$