Question

Simplify::
(a)${100}^{\frac{1}{2}}$

(b)${27}^{\frac{1}{3}}$

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

Short 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$3$

Step-by-step solution

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.

$=\sqrt[4]{3^4}$

$=3$