Chapter A.1, Problem 43E

Solution

Convert to exponential form.

  ${(a+2b)}^{\frac{2}{3}}$ .

Given:

The given expression is $\sqrt[3]{{(a+2b)}^2}$ .

Concept Used:

• The exponential form is an easier way of writing repeated multiplication involving base and exponents.

Calculation:

The given expression is $\sqrt[3]{{(a+2b)}^2}$ .

  $\begin{array}{c}\sqrt[3]{{(a+2b)}^2}={\left({(a+2b)}^2\right)}^{1/3}\\ $ ={(a+2b)}^{2\cdot \frac{1}{3}}$$ ={(a+2b)}^{\frac{2}{3}}$\end{array}$

Thus the exponential form of $\sqrt[3]{{(a+2b)}^2}$ is ${(a+2b)}^{\frac{2}{3}}$ .