Question

Which of the following expressions is equivalent to that expression?

A.(n+4)^5

B.(n+4)^1/5

C.(n+4)^5/3

D.(n+4)^3/5

Answer 1

Option D:

$(n+4)^{\frac{3}{5}}$ is the equivalent expression for $\sqrt[5]{(n+4)^{3}}$.

Solution:

Given expression:

$\sqrt[5]{(n+4)^{3}}$

To find the equivalent expression for the given expression.

$\sqrt[5]{(n+4)^{3}}$

Using radical rule: $\sqrt[m]{a}=a^{\frac{1}{m}}$

      $=\left((n+4)^{3}\right)^{\frac{1}{5}}$

Using exponent rule: $\left(a^{b}\right)^{c}=a^{b c}$

      $=(n+4)^{3 \cdot \frac{1}{5}}$

      $=(n+4)^{\frac{3}{5}}$

$\sqrt[5]{(n+4)^{3}}=(n+4)^{\frac{3}{5}}$

Hence $(n+4)^{\frac{3}{5}}$ is the equivalent expression for $\sqrt[5]{(n+4)^{3}}$.

Option D is the correct answer.