# Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 12

7

#### 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: $a^{m/n}=(a^{1/n})^{m} = \sqrt[n]{a^{m}}$ ----------------------------- $(\displaystyle \frac{7^{-12}\cdot 7^{3}}{7^{-8}})^{-1}$= ... P1... $=(\displaystyle \frac{7^{-12+3}}{7^{-8}})^{-1}=(\frac{7^{-9}}{7^{-8}})^{-1}$ = ...P2... =$(7^{-9-(-8)})^{-1}=(7^{-1})^{-1}$ = ... P3... =$7^{-1(-1)}=7^{1}$= ...P0... = $7$

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