Chapter 13.3, Problem 74STP

To determine

To find: Evaluate each expression.

Answer to Problem 74STP

  ${27}^{\frac{4}{3}}=81$

Explanation of Solution

Given information:

  ${27}^{\frac{4}{3}}$

Given

  ${27}^{\frac{4}{3}}$

  $\begin{array}{l}{27}^{\frac{4}{3}}={\left(3^3\right)}^{\frac{4}{3}}\\ \Rightarrow {27}^{\frac{4}{3}}=3^{3\times \frac{4}{3}}\\ \Rightarrow {27}^{\frac{4}{3}}=3^4\\ \Rightarrow {27}^{\frac{4}{3}}=81\end{array}$

Therefore,

  ${27}^{\frac{4}{3}}=81$