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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 8.55 (page 1069)

Simplify::
(a) $36^{\frac{1}{2}}$
(b) $8^{\frac{1}{3}}$
(c) $16^{\frac{1}{4}}$

Short Answer

Expert verified

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

01

Part (a) Step 1. Given

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

To simplify the expression.

02

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.

$= \sqrt{6^{2}}$

$= 6$

03

Part (b) Step 1. Given

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

To simplify the expression.

04

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.

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

$= 2$

05

Part (c) Step 1. Given

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

To simplify the expression.

06

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.

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

$= 2$

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Most popular questions from this chapter

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