Question

Which of the following is the rational exponent expression of ^3 to the square root of 4n?

A. (4n)^3

B. 3n^4

C. (4n)^1/3

D. 4n^1/3

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ \sqrt[3]{4n}\implies \sqrt[3]{(4n)^1}\implies (4n)^{\frac{1}{3}}$

Answer 2

The root index becomes the denominator of the rational fraction power. The appropriate choice is

... C. (4n)^(1/3)

_____

The Order of Operations requires you evaluate (4n)^1/3 as ((4n)^1)/3 = (4/3)n. That is not what you intend. Parentheses are required around any exponent that contains any kind of arithmetic operation.