Simplify 4xy^2*0^4(-y)^-3

$4 x y^{2} \cdot 0^{4} {(- y)}^{- 3}$

Step 1

Raising $0$ to any positive power yields $0$ .

$4 x y^{2} \cdot (0 {(- y)}^{- 3})$

Step 2

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

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

Step 3

Simplify the denominator.

Apply the product rule to $- y$ .

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

Raise $- 1$ to the power of $3$ .

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

Step 4

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

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

Move the negative in front of the fraction.

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

Step 5

Multiply $0 (- \frac{1}{y^{3}})$ .

Multiply $- 1$ by $0$ .

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

Multiply $0$ by $\frac{1}{y^{3}}$ .

$4 x y^{2} \cdot 0$

Step 6

Multiply $4 x y^{2} \cdot 0$ .

Multiply $0$ by $4$ .

$0 x y^{2}$

Multiply $0$ by $x$ .

$0 y^{2}$

Multiply $0$ by $y^{2}$ .

$0$