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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.16 (page 751)

Simplify: $(a) \sqrt{m^{4}} (b) \sqrt{b^{10}}$

Short Answer

Expert verified

The solution of (a) and (b) are $m^{2} a n d |b^{5}|$ respectively.

Step by step solution

01

Part (a) Step 1. Given information

The root: $\sqrt{m^{4}}$

02

Part (a) Step 2. Calculation

We have,

$\sqrt{m^{4}} = \sqrt{{(m^{2})}^{2}} \sin c e {(m^{2})}^{2} = m^{4} = m^{2}$

In this case, the absolute value sign is not needed as $m^{2}$ is positive.

Therefore, the solution is $m^{2}$

03

Part (b) Step 1. Given information

The root: $\sqrt{b^{10}}$

04

Part (b) Step 2. Calculation

We have,

$\sqrt{b^{10}} = \sqrt{{(b^{5})}^{2}} \sin c e {(b^{5})}^{2} = b^{10} = |b^{5}| \sin c e t h e i n d e x n i s e v e n \sqrt{a^{n}} = |a|$

Therefore, the solution is $|b^{5}|$

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Most popular questions from this chapter

Simplify:

a. $y^{\frac{3}{4}} 路 y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

In the following exercises, simplify using absolute value signs as needed.

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