Simplify (-2x^6y^-7)(5x^-1y)

$(- 2 x^{6} y^{- 7}) (5 x^{- 1} y)$

Step 1

Multiply $x^{6}$ by $x^{- 1}$ by adding the exponents.

Move $x^{- 1}$ .

$- 2 (x^{- 1} x^{6}) y^{- 7} (5 y)$

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

$- 2 x^{- 1 + 6} y^{- 7} (5 y)$

Add $- 1$ and $6$ .

$- 2 x^{5} y^{- 7} (5 y)$

Step 2

Multiply $y^{- 7}$ by $y$ by adding the exponents.

Move $y$ .

$- 2 x^{5} (y \cdot y^{- 7}) \cdot 5$

Multiply $y$ by $y^{- 7}$ .

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

$- 2 x^{5} (y^{1} y^{- 7}) \cdot 5$

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

$- 2 x^{5} y^{1 - 7} \cdot 5$

Subtract $7$ from $1$ .

$- 2 x^{5} y^{- 6} \cdot 5$

Step 3

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

$- 2 x^{5} \frac{1}{y^{6}} \cdot 5$

Step 4

Multiply $- 2 x^{5} \frac{1}{y^{6}}$ .

Combine $- 2$ and $\frac{1}{y^{6}}$ .

$x^{5} \frac{- 2}{y^{6}} \cdot 5$

Combine $x^{5}$ and $\frac{- 2}{y^{6}}$ .

$\frac{x^{5} \cdot - 2}{y^{6}} \cdot 5$

Step 5

Simplify the expression.

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

$\frac{- 2 \cdot x^{5}}{y^{6}} \cdot 5$

Move the negative in front of the fraction.

$- \frac{(2) \cdot x^{5}}{y^{6}} \cdot 5$

Step 6

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

$- \frac{2 x^{5}}{y^{6}} \cdot 5$

Step 7

Multiply $- \frac{2 x^{5}}{y^{6}} \cdot 5$ .

Multiply $5$ by $- 1$ .

$- 5 \frac{2 x^{5}}{y^{6}}$

Combine $- 5$ and $\frac{2 x^{5}}{y^{6}}$ .

$\frac{- 5 (2 x^{5})}{y^{6}}$

Multiply $2$ by $- 5$ .

$\frac{- 10 x^{5}}{y^{6}}$

Step 8

Move the negative in front of the fraction.

$- \frac{10 x^{5}}{y^{6}}$

Simplify (-2x^6y^-7)(5x^-1y)

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