Simplify. Write expression using only positive exponent.
$\frac{3^{- 1} \cdot z^{5}}{z^{- 2}}$

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Solution

Simplifying the expression
$\frac{3^{- 1} \cdot z^{5}}{z^{- 2}}$
$= 3^{- 1} \cdot z^{5} \cdot z^{- 2}$ (Using exponent law $\frac{1}{a^{- n}} = a^{n}$ )
$= 3^{- 1} \cdot z^{5 + (- 2)}$ (Using exponent law $a^{m} \cdot a^{n} = a^{m + n}$ )
$= 3^{- 1} \cdot z^{5 - 2}$
$= 3^{- 1} \cdot z^{3}$
$= \frac{1}{3} \cdot z^{3}$ (Using exponent law $\frac{1}{a^{- n}} = a^{n}$ )
$= \frac{z^{3}}{3}$
Hence, the expression is $\frac{3^{- 1} \cdot z^{5}}{z^{- 2}} = \frac{z^{3}}{3}$

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