Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.1 - Properties of Radicals - Exercises - Page 488: 115

Answer

$x=-\frac{2}{3}$

Work Step by Step

$(625)^{x}=(\frac{1}{25})^{x+2}$ Rewriting $625$ as $25^{2}$ and $\frac{1}{25}$ as $25^{-1}$, we have $(25^{2})^{x}=(25^{-1})^{x+2}$ $\implies 25^{2x}=25^{-x-2}$ $\implies 2x=-x-2$ $\implies 2x+x=-2$ or $3x=-2$ $\implies x=-\frac{2}{3}$ Check: $(625)^{-\frac{2}{3}}=(25^2)^{-\frac{2}{3}}=\left(\frac{1}{25}\right)^{\frac{4}{3}}$ $\left(\frac{1}{25}\right)^{(-\frac{2}{3}+2)}=\left(\frac{1}{25}\right)^{\frac{4}{3}}$
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