Simplify (z^(-1/3))/(z^(-5/6))

$\frac{z^{- \frac{1}{3}}}{z^{- \frac{5}{6}}}$

Move $z^{- \frac{5}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$z^{- \frac{1}{3}} z^{\frac{5}{6}}$

Multiply $z^{- \frac{1}{3}}$ by $z^{\frac{5}{6}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{- \frac{1}{3} + \frac{5}{6}}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z^{- \frac{1}{3} \cdot \frac{2}{2} + \frac{5}{6}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$z^{- \frac{2}{3 \cdot 2} + \frac{5}{6}}$

Multiply $3$ by $2$ .

$z^{- \frac{2}{6} + \frac{5}{6}}$

Combine the numerators over the common denominator.

$z^{\frac{- 2 + 5}{6}}$

Add $- 2$ and $5$ .

$z^{\frac{3}{6}}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$z^{\frac{3 (1)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$z^{\frac{3 \cdot 1}{3 \cdot 2}}$

Cancel the common factor.

$z^{\frac{3 \cdot 1}{3 \cdot 2}}$

Rewrite the expression.

$z^{\frac{1}{2}}$