Simplify (z^(-1/4)z^(5/4))/(z^(1/3))

$\frac{z^{- \frac{1}{4}} z^{\frac{5}{4}}}{z^{\frac{1}{3}}}$

Step 1

Multiply $z^{- \frac{1}{4}}$ by $z^{\frac{5}{4}}$ by adding the exponents.

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

$\frac{z^{- \frac{1}{4} + \frac{5}{4}}}{z^{\frac{1}{3}}}$

Combine the numerators over the common denominator.

$\frac{z^{\frac{- 1 + 5}{4}}}{z^{\frac{1}{3}}}$

Add $- 1$ and $5$ .

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

Divide $4$ by $4$ .

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

Step 2

Simplify $z^{1}$ .

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

Step 3

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

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

Step 4

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

Multiply $z$ by $z^{- \frac{1}{3}}$ .

Raise $z$ to the power of $1$ .

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

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

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $3$ .

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