Simplify (2xy^-1z^0)/(-4x^3y^2)

$\frac{2 x y^{- 1} z^{0}}{- 4 x^{3} y^{2}}$

Move $y^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 x}{- 4 x^{3} y^{2} y}$

Multiply $y^{2}$ by $y$ by adding the exponents.

Move $y$ .

$\frac{2 x}{- 4 x^{3} (y \cdot y^{2})}$

Multiply $y$ by $y^{2}$ .

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

$\frac{2 x}{- 4 x^{3} (y^{1} y^{2})}$

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

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

Add $1$ and $2$ .

$\frac{2 x}{- 4 x^{3} y^{3}}$

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{- 4 x^{3} y^{3}}$

Cancel the common factors.

Factor $2$ out of $- 4 x^{3} y^{3}$ .

$\frac{2 (x)}{2 (- 2 x^{3} y^{3})}$

Cancel the common factor.

$\frac{2 x}{2 (- 2 x^{3} y^{3})}$

Rewrite the expression.

$\frac{x}{- 2 x^{3} y^{3}}$

Cancel the common factor of $x$ and $x^{3}$ .

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

$\frac{x^{1}}{- 2 x^{3} y^{3}}$

Factor $x$ out of $x^{1}$ .

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

Cancel the common factors.

Factor $x$ out of $- 2 x^{3} y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{- 2 x^{2} y^{3}}$

Move the negative in front of the fraction.

$- \frac{1}{2 x^{2} y^{3}}$