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 - Chapter Review - Page 475: 22


$m^{\frac{3}{4}}.n^{\frac{1}{2}} \times m^{\frac{1}{2}}n^{\frac{1}{2}}=m^{\frac{5}{4}}.n$

Work Step by Step

$m^{\frac{3}{4}}.n^{\frac{1}{2}} \times m^xn^y=m^{\frac{5}{4}}.n$ $m^{(\frac{3}{4}+x)}.n^{(\frac{1}{2}+y)}=m^{\frac{5}{4}}.n^1$ Multiply the powers with the same base. $\frac{3}{4}+x=\frac{5}{4}$ $x=\frac{1}{2}$ and $\frac{1}{2}+y=1$ $y=\frac{1}{2}$ Therefore, the completed equation is: $m^{\frac{3}{4}}.n^{\frac{1}{2}} \times m^{\frac{1}{2}}n^{\frac{1}{2}}=m^{\frac{5}{4}}.n$
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