College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises - Page 76: 88



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $ 3^{-1}-4^{-1} .$ Then change the resulting fractions to similar fractions. $\bf{\text{Solution Details:}}$ Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{3^1}-\dfrac{1}{4^1} \\\\= \dfrac{1}{3}-\dfrac{1}{4} .\end{array} To subtract the expression above, make the fractions similar (same denominator) by multiplying each term by an expression equal to $1$. The expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{3}\cdot\dfrac{4}{4}-\dfrac{1}{4}\cdot\dfrac{3}{3} \\\\= \dfrac{4}{12}-\dfrac{3}{12} \\\\= \dfrac{4-3}{12} \\\\= \dfrac{1}{12} .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.