Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-4 Division Properties of Exponents - Practice and Problem-Solving Exercises - Page 444: 81


$x=7$ $y=4$

Work Step by Step

$\frac{a^x}{a^y}=a^3$ $a^{x-y}=a^3$ Comparing the exponents of a on both sides: $x-y=3$ (1) $\frac{a^x}{a^3y}=a^{-5}$ $a^{x-3y}=a^{-5}$ Comparing the exponents of a on both sides: $x-3y=-5$ (2) From (1) and (2) we get: $x-y=3$ $x-3y=-5$ Multiply both sides of the second equation with $-1$: $x-y=3$ $-x+3y=5$ Using substitution: $2y=8$ Solve for $y$: $y=4$ Solve for $x$: $x-4=3$ $x=7$
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