Simplify (-5x^3y^2)(-2x^-11y^-2)

$(- 5 x^{3} y^{2}) (- 2 x^{- 11} y^{- 2})$

Multiply $x^{3}$ by $x^{- 11}$ by adding the exponents.

Move $x^{- 11}$ .

$- 5 (x^{- 11} x^{3}) y^{2} (- 2 y^{- 2})$

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

$- 5 x^{- 11 + 3} y^{2} (- 2 y^{- 2})$

Add $- 11$ and $3$ .

$- 5 x^{- 8} y^{2} (- 2 y^{- 2})$

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

Move $y^{- 2}$ .

$- 5 x^{- 8} (y^{- 2} y^{2}) \cdot - 2$

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

$- 5 x^{- 8} y^{- 2 + 2} \cdot - 2$

Add $- 2$ and $2$ .

$- 5 x^{- 8} y^{0} \cdot - 2$

Simplify $- 5 x^{- 8} y^{0} \cdot - 2$ .

$- 5 x^{- 8} \cdot - 2$

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

$- 5 \frac{1}{x^{8}} \cdot - 2$

Combine $- 5$ and $\frac{1}{x^{8}}$ .

$\frac{- 5}{x^{8}} \cdot - 2$

Move the negative in front of the fraction.

$- \frac{5}{x^{8}} \cdot - 2$

Multiply $- \frac{5}{x^{8}} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

$2 \frac{5}{x^{8}}$

Combine $2$ and $\frac{5}{x^{8}}$ .

$\frac{2 \cdot 5}{x^{8}}$

Multiply $2$ by $5$ .

$\frac{10}{x^{8}}$