Answer
$\displaystyle \frac{1}{3z^{7}}$
Work Step by Step
In each step, we use one of the Properties of Exponents...
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: $a^{m/n}=(a^{1/n})^{m}$=$\sqrt[n]{a^{m}}$
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$\displaystyle \frac{(3z^{2})^{-1}}{z^{5}}$= ... P$4$...
$=\displaystyle \frac{3^{-1}(z^{2})^{-1}}{z^{5}}$= ... P$3$...
=$\displaystyle \frac{3^{-1}z^{-2}}{z^{5}}=3^{-1}\cdot\frac{z^{-2}}{z^{5}}$= ... P$2$...
$=3^{-1}z^{-2-5}=3^{-1}z^{-7}$= ... P$2$...
$=\displaystyle \frac{1}{3}\cdot\frac{1}{z^{7}}$
$= \displaystyle \frac{1}{3z^{7}}$
