Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 18


$\displaystyle \frac{m^{3}}{625}$

Work Step by Step

We use the Properties of Exponents, step by step... P0. $a^{0}=1,\ a^{1}=a$ P1. $a^{m}\cdot a^{n}=a^{m+n}$ P2. $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ , $ \displaystyle \frac{1}{a^{n}}=a^{-n}$ P3. $(a^{m})^{n}=a^{mn}$ P4. $(ab)^{m}=a^{m} b^{m}$ P5. $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$ P6. Rational exponents: $a^{m/n}=(a^{1/n})^{m}\sqrt[n]{a^{m}}$ ----------------------------- $\displaystyle \frac{5^{-2}m^{2}y^{-2}}{5^{2}m^{-1}y^{-2}}=\frac{5^{-2}}{5^{2}}\cdot\frac{m^{2}}{m^{-1}}\cdot\frac{y^{-2}}{y^{-2}}$= ... P2... $5^{-2-2}m^{2-(-1)}y^{-2-(-2)}=5^{-4}m^{3}y^{0}$= ... P0... $=5^{-4}m^{3}\cdot 1$= ... P2...$=\displaystyle \frac{1}{5^{4}}\cdot m^{3}$ $= \displaystyle \frac{m^{3}}{625}$
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