Simplify -7xy^-2*xy

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

Step 1

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 2

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

Move $y$ .

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

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

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

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

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

$- 7 x^{2} y^{1 - 2}$

Subtract $2$ from $1$ .

$- 7 x^{2} y^{- 1}$

Step 3

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

$- 7 x^{2} \frac{1}{y}$

Step 4

Multiply $- 7 x^{2} \frac{1}{y}$ .

Combine $- 7$ and $\frac{1}{y}$ .

$x^{2} \frac{- 7}{y}$

Combine $x^{2}$ and $\frac{- 7}{y}$ .

$\frac{x^{2} \cdot - 7}{y}$

Step 5

Move $- 7$ to the left of $x^{2}$ .

$\frac{- 7 \cdot x^{2}}{y}$

Step 6

Move the negative in front of the fraction.

$- \frac{7 x^{2}}{y}$