Simplify (-5x^3y^-4)(2x^-1y)

$(- 5 x^{3} y^{- 4}) (2 x^{- 1} y)$

Step 1

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

Move $x^{- 1}$ .

$- 5 (x^{- 1} x^{3}) y^{- 4} (2 y)$

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

$- 5 x^{- 1 + 3} y^{- 4} (2 y)$

Add $- 1$ and $3$ .

$- 5 x^{2} y^{- 4} (2 y)$

Step 2

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

Move $y$ .

$- 5 x^{2} (y \cdot y^{- 4}) \cdot 2$

Multiply $y$ by $y^{- 4}$ .

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

$- 5 x^{2} (y^{1} y^{- 4}) \cdot 2$

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

$- 5 x^{2} y^{1 - 4} \cdot 2$

Subtract $4$ from $1$ .

$- 5 x^{2} y^{- 3} \cdot 2$

Step 3

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

$- 5 x^{2} \frac{1}{y^{3}} \cdot 2$

Step 4

Multiply $- 5 x^{2} \frac{1}{y^{3}}$ .

Combine $- 5$ and $\frac{1}{y^{3}}$ .

$x^{2} \frac{- 5}{y^{3}} \cdot 2$

Combine $x^{2}$ and $\frac{- 5}{y^{3}}$ .

$\frac{x^{2} \cdot - 5}{y^{3}} \cdot 2$

Step 5

Simplify the expression.

Move $- 5$ to the left of $x^{2}$ .

$\frac{- 5 \cdot x^{2}}{y^{3}} \cdot 2$

Move the negative in front of the fraction.

$- \frac{(5) \cdot x^{2}}{y^{3}} \cdot 2$

Step 6

Multiply $5$ by $x^{2}$ .

$- \frac{5 x^{2}}{y^{3}} \cdot 2$

Step 7

Multiply $- \frac{5 x^{2}}{y^{3}} \cdot 2$ .

Multiply $2$ by $- 1$ .

$- 2 \frac{5 x^{2}}{y^{3}}$

Combine $- 2$ and $\frac{5 x^{2}}{y^{3}}$ .

$\frac{- 2 (5 x^{2})}{y^{3}}$

Multiply $5$ by $- 2$ .

$\frac{- 10 x^{2}}{y^{3}}$

Step 8

Move the negative in front of the fraction.

$- \frac{10 x^{2}}{y^{3}}$

Simplify (-5x^3y^-4)(2x^-1y)

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