Question

Show two different algebraic methods to simplify $4^{\frac{3}{2}}$. Explain all your steps.

Short answer

1. Simplify the expression with $a^{\frac{1}{n}}$.
2. Simplify the expression with $a^{\frac{m}{n}}$.
3. $4^{\frac{3}{2}}=8$
   

Step-by-step solution

Step 1. Given Information 

We are given an expression $4^{\frac{3}{2}}$.

Step 2. Explanation

Simplify the expression with $a^{\frac{1}{n}}=\sqrt[n]{a}$.

Simplify the expression with $a^{\frac{m}{n}}=\sqrt[n]{a^m}$.

$$\begin{gathered} 4^{\frac{3}{2}}=\sqrt[2]{4^3} \\ {4}^{\frac{3}{2}}=\sqrt[2]{64} \\ {4}^{\frac{3}{2}}=8 \end{gathered}$$