Evaluate (4x^0y^-2z^3)/(4x)

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

Move $x^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Simplify the denominator.

Multiply $x$ by $x^{0}$ by adding the exponents.

Move $x^{0}$ .

$\frac{4 z^{3}}{4 (x^{0} x) y^{2}}$

Multiply $x^{0}$ by $x$ .

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

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

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

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

Add $0$ and $1$ .

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

Simplify $4 x^{1}$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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