Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 81: 140

Answer

The negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ says that a term with a negative exponent becomes the same term with a positive exponent if it is moved across the fraction bar—from numerator to denominator or vice versa. For instance, consider $\frac{x^{-2}}{y^{-3}}$. In simplifying this, move $x^{-2}$ to the denominator and change the power to $+2$. Do the same for $y^{-3}$, move it to the numerator and change the exponent to $+3$. Thus, $$\frac{x^{-2}}{y^{-3}} =\frac{y^{3}}{x^{2}}$$

Work Step by Step

The negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ says that a term with a negative exponent becomes the same term with a positive exponent if it is moved across the fraction bar—from numerator to denominator or vice versa. For instance, consider $\frac{x^{-2}}{y^{-3}}$. In simplifying this, move $x^{-2}$ to the denominator and change the power to $+2$. Do the same for $y^{-3}$, move it to the numerator and change the exponent to $+3$. Thus, $$\frac{x^{-2}}{y^{-3}} =\frac{y^{3}}{x^{2}}$$
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