Simplify (-4x^-6y^8)(-6x^-4y^-2)

$(- 4 x^{- 6} y^{8}) (- 6 x^{- 4} y^{- 2})$

Step 1

Multiply $x^{- 6}$ by $x^{- 4}$ by adding the exponents.

Move $x^{- 4}$ .

$- 4 (x^{- 4} x^{- 6}) y^{8} (- 6 y^{- 2})$

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

$- 4 x^{- 4 - 6} y^{8} (- 6 y^{- 2})$

Subtract $6$ from $- 4$ .

$- 4 x^{- 10} y^{8} (- 6 y^{- 2})$

Step 2

Multiply $y^{8}$ by $y^{- 2}$ by adding the exponents.

Move $y^{- 2}$ .

$- 4 x^{- 10} (y^{- 2} y^{8}) \cdot - 6$

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

$- 4 x^{- 10} y^{- 2 + 8} \cdot - 6$

Add $- 2$ and $8$ .

$- 4 x^{- 10} y^{6} \cdot - 6$

Step 3

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

$- 4 \frac{1}{x^{10}} y^{6} \cdot - 6$

Step 4

Combine $- 4$ and $\frac{1}{x^{10}}$ .

$\frac{- 4}{x^{10}} y^{6} \cdot - 6$

Step 5

Move the negative in front of the fraction.

$- \frac{4}{x^{10}} y^{6} \cdot - 6$

Step 6

Combine $y^{6}$ and $\frac{4}{x^{10}}$ .

$- \frac{y^{6} \cdot 4}{x^{10}} \cdot - 6$

Step 7

Move $4$ to the left of $y^{6}$ .

$- \frac{4 \cdot y^{6}}{x^{10}} \cdot - 6$

Step 8

Multiply $- \frac{4 y^{6}}{x^{10}} \cdot - 6$ .

Multiply $- 6$ by $- 1$ .

$6 \frac{4 y^{6}}{x^{10}}$

Combine $6$ and $\frac{4 y^{6}}{x^{10}}$ .

$\frac{6 (4 y^{6})}{x^{10}}$

Multiply $4$ by $6$ .

$\frac{24 y^{6}}{x^{10}}$