Question

Simplify::
(a)${36}^{\frac{1}{2}}$

(b)$8^{\frac{1}{3}}$

(c)${16}^{\frac{1}{4}}$

Short answer

The simplification of ${36}^{\frac{1}{2}}$is$6$

The simplification of $8^{\frac{1}{3}}$is$2$

The simplification of ${16}^{\frac{1}{4}}$is $2$

Step-by-step solution

Part (a) Step 1. Given

An expression ${36}^{\frac{1}{2}}$

To simplify the expression.

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

Rewrite as a square root.

${36}^{\frac{1}{2}}=\sqrt{36}$

Recognize $36$as a perfect square.

$=\sqrt{6^2}$

$=6$

Part (b) Step 1. Given

An expression $8^{\frac{1}{3}}$

To simplify the expression.

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

Rewrite as a cube root.

$8^{\frac{1}{3}}=\sqrt[3]{8}$

Recognize $8$as a perfect cube.

$=\sqrt[3]{2^3}$

$=2$

Part (c) Step 1. Given

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

To simplify the expression.

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

Rewrite as a fourth root.

${16}^{\frac{1}{4}}=\sqrt[4]{16}$

Recognize $16$as a perfect fourth power.

$=\sqrt[4]{2^4}$

$=2$