Q 129E - Intermediate Algebra

Question

In the following exercises, simplify.

Part (a): ${81}^{\frac{1}{2}}$

Part (b): ${125}^{\frac{1}{3}}$

Part (c): ${64}^{\frac{1}{2}}$

Step-by-Step Solution

Answer

Part (a): On simplifying, we get $9$.

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

Part (c): On simplifying, we get $8$.

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

Consider the given question,

${81}^{\frac{1}{2}}$

Rewrite as a square root,

$=\sqrt[2]{81}$

On simplifying the expression,

$=9$

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

Consider the given question,

${125}^{\frac{1}{3}}$

Rewrite as a cube root,

$=\sqrt[3]{125}$

On simplifying the expression,

$=5$

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

Consider the given question,

${64}^{\frac{1}{2}}$

Rewrite as a square root,

$=\sqrt[2]{64}$

On simplifying the expression,

$=8$