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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. 468 (page 562)

In the following exercise, divide the monomials
$\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}}$

Short Answer

Expert verified

The simplified form of $\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}}$ is $\frac{u^{4}}{5 v^{5}}$ .

Step by step solution

01

. Given information

$\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}}$

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

$\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}} = \frac{11}{55} 脳 \frac{u^{6}}{u^{2}} 脳 \frac{v^{3}}{v^{8}} = \frac{1}{5} 脳 u^{6 - 2} 脳 v^{3 - 8} u \sin g q u o t i e n t p r o p e r t y = \frac{1}{5} 脳 u^{4} 脳 v^{- 5} = \frac{1}{5} 脳 \frac{u^{4}}{v^{5}} u \sin g n e g a t i v e e x p o n e n t p r o p e r t y = \frac{u^{4}}{5 v^{5}}$

Thus simplified form of $\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}} i s \frac{u^{4}}{5 v^{5}} .$

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