Simplify 4x^2y^3(2x^-4y)

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

Step 1

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

Move $x^{- 4}$ .

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

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

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

Add $- 4$ and $2$ .

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

Step 2

Multiply $y^{3}$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

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

Multiply $2$ by $4$ .

$\frac{8 y^{4}}{x^{2}}$