Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Review Exercises - Page 416: 85



Work Step by Step

Use the product rule, which states that if you raise a power to a power, you simply multiply the powers together: $$\frac{x^{(7)(-2)}}{x^{(4)(-2)}}$$ We can now multiply the exponents in both the numerator and denominator: $$\frac{x^{-14}}{x^{-8}}$$ Now use the quotient rule to simplify the fraction. With the quotient rule, you subtract the power of the denominator from the power of the numerator, provided the bases are the same: $$x^{(-14 - (-8))}$$ Simplify the exponents: $$x^{-6}$$ To get rid of the negative exponents, you replace the expression with its inverse: $$\frac{1}{x^6}$$
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