Chapter 16.5, Problem 4MRE

To determine

To simplify: the given expression.

Answer to Problem 4MRE

The simplified form of the expression is $a^2$ .

Explanation of Solution

Given information:

Given expression,

  $\sqrt[3]{a^2}\cdot \sqrt[3]{a^4}$

Calculation:

Consider the given expression:

  $\sqrt[3]{a^2}\cdot \sqrt[3]{a^4}$

Now, simplify the expression as shown,

  $\begin{array}{c}\sqrt[3]{a^2}\cdot \sqrt[3]{a^4}=a^{\frac{2}{3}}\cdot a^{\frac{4}{3}}\\ =a^{\frac{2}{3}+\frac{4}{3}}\\ =a^{\frac{6}{3}}\\ =a^2\end{array}$

Hence, the simplified form of the expressionis $a^2$ .