Question

How do you evaluate and simplify ${27}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$?

Answer 1

Simplify the given term ${27}^{\frac{2}{3}}$

$27$ can be expressed in the power of $3$

$$\begin{gathered} 27=3\times 3\times 3 \\ 27=3^3 \end{gathered}$$

So the given number becomes

$$\begin{gathered} {27}^{\frac{2}{3}}={\left(3^3\right)}^{\frac{2}{3}} \\ {27}^{\frac{2}{3}}={\left(3\right)}^2 \\ {27}^{\frac{2}{3}}=9 \end{gathered}$$

Hence the answer is $9$