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 - Page 445: 85



Work Step by Step

Given : $\frac{27x^{3}}{8y^{3}}$ Now, $27=3^{3}$ and $8=2^{3}$ Hence, the expression can be written as : $\frac{3^{3}x^{3}}{2^{3}y^{3}}$ Since $a^{m}b^{m}=$ $(ab)^{m}$, hence $3^{3}x^{3}=$ $(3x)^{3}$ and $2^{3}y^{3}=$ $(2y)^{3}$ Thus, this becomes : $\frac{(3x)^{3}}{(2y)^{3}}$ This becomes : $(\frac{3x}{2y}$$)^{3}$ (since $\frac{a^{m}}{b^{m}}=$ ($\frac{a}{b}$$)^{m}$)
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