Question

$4^3=\_\_\_\_\_\_\_;8^{2/3}=\_\_\_\_\_\_\_;3^{-2}=\_\_\_\_\_\_\_$

Short answer

The answer of$$\begin{gathered} 4^3=64 \\ {8}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=4 \\ {3}^{-2}=\frac{1}{9} \end{gathered}$$.

Step-by-step solution

Step 1. Solving the given expression

We can write $4^3$as $4\times 4\times 4$.

The solution is$4\times 4\times 4=64.$

Step 2. Solving the given expression

By the laws of exponent,$a^{\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}=\sqrt[n]{a^m}$.

So,

$$\begin{gathered} 8^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=\sqrt[3]{8^2} \\ =\sqrt[3]{64} \\ =\sqrt[3]{{\left(4\right)}^3} \\ =4 \end{gathered}$$

Step 3. Solving the given expression 

By the laws of exponent, $a^{-x}=\frac{1}{a^x}$.

So,

$$\begin{gathered} 3^{-2}=\frac{1}{3^2} \\ =\frac{1}{9} \end{gathered}$$