Simplify (z^(-1/2)z^(5/2))/(z^(1/3))

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

Step 1

Multiply $z^{- \frac{1}{2}}$ by $z^{\frac{5}{2}}$ by adding the exponents.

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

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

Combine the numerators over the common denominator.

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

Add $- 1$ and $5$ .

$\frac{z^{\frac{4}{2}}}{z^{\frac{1}{3}}}$

Divide $4$ by $2$ .

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

Step 2

Move $z^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 3

Multiply $z^{2}$ by $z^{- \frac{1}{3}}$ by adding the exponents.

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

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

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

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

Combine $2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

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

Subtract $1$ from $6$ .

$z^{\frac{5}{3}}$