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: 15



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: $a^{m/n}=(a^{1/n})^{m}\sqrt[n]{a^{m}}$ ----------------------------- $\displaystyle \frac{(4k^{-1})^{2}}{2k^{-5}}$= ... P$4$... $=\displaystyle \frac{4^{2}(k^{-1})^{2}}{2k^{-5}}$= ... P$3$... $=\displaystyle \frac{16}{2}\cdot\frac{k^{-2}}{k^{-5}}$= ... P$2$... $=8k^{-2-(-5)}=8k^{-2+5}=8k^{3}$
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