Chapter 6.2, Problem 50E

To determine

To find: a formula that contains a radical and then rewrites it using rational exponents.

Answer to Problem 50E

  $s=V^{\frac{1}{3}}$

Explanation of Solution

Concept used:

  $\sqrt[n]{a}=a^{\frac{1}{n}}$

The side length of a cube of volume V is given by the formula:

  $s=\sqrt[3]{V}$

Using the fact that $\sqrt[n]{a}=a^{\frac{1}{n}}$ ,

  $\begin{array}{c}s=\sqrt[3]{V}\\ =V^{\frac{1}{3}}\end{array}$