Chapter 11.3, Problem 43E

To determine

To calculate:

The value of the following without using a calculator:

  ${27}^{\frac{2}{3}}$

Answer to Problem 43E

The given expression is evaluated as $3^2$ .

Explanation of Solution

Given information:

  ${27}^{\frac{2}{3}}$

Calculation:

The given expression is:

  $\begin{array}{l}{27}^{\frac{2}{3}}={\left(27\right)}^{\frac{2}{3}}\\ {27}^{\frac{2}{3}}={\left(3^3\right)}^{\frac{2}{3}}\\ {27}^{\frac{2}{3}}=3^{3\cdot \frac{2}{3}}\\ {27}^{\frac{2}{3}}=3^2\end{array}$