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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. 466 (page 562)

In the following exercise, divide the monomials. $\frac{- 30 x^{8}}{- 36 x^{9}}$

Short Answer

Expert verified

The simplified form is $\frac{5}{6 x} o r \frac{5}{6} x^{- 1}$ .

Step by step solution

01

Step 1. Given information

The monomials : $\frac{- 30 x^{8}}{- 36 x^{9}}$

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

$\frac{- 30 x^{8}}{- 36 x^{9}} = \frac{- 30}{- 36} 脳 \frac{x^{8}}{x^{9}} = \frac{- 6 脳 5}{- 6 脳 6} 脳 \frac{x^{8}}{x^{9}} = \frac{5}{6} 脳 x^{8 - 9} u \sin g Q u o t i e n t p r o p e r t y . = \frac{5}{6} 脳 x^{- 1} = \frac{5}{6 x} U \sin g N e g a t i v e e x p o n e n t p r o p e r t y .$

Thus simplified form of $\frac{- 30 x^{8}}{- 36 x^{9}}$ is $\frac{5}{6 x} o r \frac{5}{6} x^{- 1}$ .

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