Simplify (z^2z^4)/(z^3z^-1)

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

Step 1

Multiply $z^{2}$ by $z^{4}$ by adding the exponents.

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

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

Add $2$ and $4$ .

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

Step 2

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

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

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

Subtract $1$ from $3$ .

$\frac{z^{6}}{z^{2}}$

Step 3

Cancel the common factor of $z^{6}$ and $z^{2}$ .

Factor $z^{2}$ out of $z^{6}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $z^{4}$ by $1$ .

$z^{4}$