Q. 8.56 - Intermediate Algebra

Question

Simplify::
(a) ${100}^{\frac{1}{2}}$

(b) ${27}^{\frac{1}{3}}$

(c) ${81}^{\frac{1}{4}}$

Step-by-Step Solution

Answer

The simplification of ${100}^{\frac{1}{2}}$ is $10$

The simplification of ${27}^{\frac{1}{3}}$ is $3$

The simplification of ${81}^{\frac{1}{4}}$ is $3$

Part (a) Step 1. Given

An expression ${100}^{\frac{1}{2}}$

To simplify the expression.

Part (a) Step 2. Rewrite as perfect nth power

Rewrite as a square root. 

${100}^{\frac{1}{2}}=\sqrt{100}$

Recognize $100$ as a perfect square.

           $=\sqrt{{10}^2}$

           $=10$

Part (b) Step 1. Given

An expression ${27}^{\frac{1}{3}}$

To simplify the expression.

Part (b) Step 2. Rewrite as perfect nth power

Rewrite as a cube root.

${27}^{\frac{1}{3}}=\sqrt[3]{27}$

Recognize $27$ as a perfect cube.

         $=\sqrt[3]{3^3}$

         $=3$

Part (c) Step 1. Given

An expression ${81}^{\frac{1}{4}}$

To simplify the expression.

Part (c) Step 2. Rewrite as perfect nth power

Rewrite as a fourth root. 

${81}^{\frac{1}{4}}=\sqrt[4]{81}$

Recognize $81$ as a perfect fourth power.

         $=\sqrt[4]{3^4}$

         $=3$