Q 131E - Intermediate Algebra

Question

In the following exercises, simplify.

Part (a): ${16}^{\frac{1}{4}}$

Part (b): ${16}^{\frac{1}{2}}$

Part (c): ${625}^{\frac{1}{4}}$

Step-by-Step Solution

Answer

Part (a): On simplifying, we get $2$.

Part (b): On simplifying, we get $4$.

Part (c): On simplifying, we get $5$.

Part (a) Step 1. Rewrite as a root.

Consider the given question,

${16}^{\frac{1}{4}}$

Rewrite as a fourth root,

$=\sqrt[4]{16}$

Recognize $16$  is a perfect fourth power. Then on simplifying the expression,

$$\begin{gathered} =\sqrt[4]{2^4} \\ =2 \end{gathered}$$

Part (b) Step 1. Rewrite as a root.

Consider the given question,

${16}^{\frac{1}{2}}$

Rewrite as a square root,

$=\sqrt[2]{16}$

On simplifying the expression,

$=4$

Part (c) Step 1. Rewrite as a root.

Consider the given question,

${625}^{\frac{1}{4}}$

Rewrite as a fourth root,

$=\sqrt[4]{625}$

Recognize $625$ is a perfect fourth power. Then on simplifying the expression,

$$\begin{gathered} =\sqrt[4]{5^4} \\ =5 \end{gathered}$$