## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises - Page 459: 7

#### Answer

$\sqrt[3]{x}\cdot\sqrt[3]{x}=\sqrt[3]{x^2}$

#### Work Step by Step

Using $\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$, the expression $\sqrt[3]{x}\cdot\sqrt[3]{x}$ is equivalent to \begin{align*} & \sqrt[3]{x\cdot x} \\&= \sqrt[3]{x^2} .\end{align*} Hence, $\sqrt[3]{x}\cdot\sqrt[3]{x}$ is equal to $\sqrt[3]{x^2}$ and not equal to $x$.

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