Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-5 Division Properties of Exponents - Practice and Problem-Solving Exercises: 81

Answer

$x=7$ and $y=4$

Work Step by Step

Given the two equations,we need to find the value of $x$ and $y$. Hence, $\frac{a^{x}}{a^{y}}=$ $a^{x-y}=$ $a^{3}$ and $\frac{a^{x}}{a^{3y}}=$ $a^{x-3y}=$ $a^{-5}$ (since $\frac{a^{m}}{a^{n}}=a^{m-n}$) Thus, Hence $x-$$y=$ $3$ and $x-$ $3y=$ $-5$ After subtracting the second equation from first, we get : $2y=$ $8$ Hence, $y=$ $4$ Substituting the value of $y$ in the first equation , we get : $x=$ $y+3=$ $4+3=$ $7$
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