Simplify zx^-3y^0*2zx^-1y^-1

$z x^{- 3} y^{0} \cdot 2 z x^{- 1} y^{- 1}$

Rewrite using the commutative property of multiplication.

$2 z x^{- 3} y^{0} (z x^{- 1} y^{- 1})$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$2 (z \cdot z) x^{- 3} y^{0} (x^{- 1} y^{- 1})$

Multiply $z$ by $z$ .

$2 z^{2} x^{- 3} y^{0} (x^{- 1} y^{- 1})$

Simplify $2 z^{2} x^{- 3} y^{0} (x^{- 1} y^{- 1})$ .

$2 z^{2} x^{- 3} (x^{- 1} y^{- 1})$

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

Move $x^{- 1}$ .

$2 z^{2} (x^{- 1} x^{- 3}) y^{- 1}$

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

$2 z^{2} x^{- 1 - 3} y^{- 1}$

Subtract $3$ from $- 1$ .

$2 z^{2} x^{- 4} y^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 z^{2} \frac{1}{x^{4}} y^{- 1}$

Multiply $2 z^{2} \frac{1}{x^{4}}$ .

Combine $2$ and $\frac{1}{x^{4}}$ .

$z^{2} \frac{2}{x^{4}} y^{- 1}$

Combine $z^{2}$ and $\frac{2}{x^{4}}$ .

$\frac{z^{2} \cdot 2}{x^{4}} y^{- 1}$

Move $2$ to the left of $z^{2}$ .

$\frac{2 \cdot z^{2}}{x^{4}} y^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Combine.

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

Multiply $2$ by $1$ .

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