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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 467 (page 562)

In the following exercise, divide the monomials
$\frac{28 a^{9} b}{7 a^{4} b^{3}}$

Short Answer

Expert verified

The simplified form of $\frac{28 a^{9} b}{7 a^{4} b^{3}}$ is $\frac{4 a^{5}}{b^{2}} o r 4 a^{5} b^{- 2}$ .

Step by step solution

01

. Given information

The monomials: $\frac{28 a^{9} b}{7 a^{4} b^{3}}$

02

Step 2. Properties of exponents

$a^{m} 脳 a^{n} = a^{m + n} P r o d u c t p r o p e r e t y \frac{a^{m}}{a^{n}} = a^{m - n} Q u o t i e n t p r o p e r t y a^{- m} = \frac{1}{a^{m}} N e g a t i v e e x p o n e n t p r o p e r t y .$

03

Step 3. Simplification

$\frac{28 a^{9} b}{7 a^{4} b^{3}} = \frac{28}{7} 脳 \frac{a^{9}}{a^{4}} 脳 \frac{b}{b^{3}} U \sin g Q u o t i e n t p r o p e r t y = 4 脳 a^{9 - 4} 脳 b^{1 - 3} = 4 a^{5} b^{- 2} = \frac{4 a^{5}}{b^{2}}$

Thus the simplified form of $\frac{28 a^{9} b}{7 a^{4} b^{3}}$ is $\frac{4 a^{5}}{b^{2}}$ .

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