Simplify (19x^-12y^6)(-4xy^7)

$(19 x^{- 12} y^{6}) (- 4 x y^{7})$

Step 1

Multiply $x^{- 12}$ by $x$ by adding the exponents.

Move $x$ .

$19 (x \cdot x^{- 12}) y^{6} (- 4 y^{7})$

Multiply $x$ by $x^{- 12}$ .

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

$19 (x^{1} x^{- 12}) y^{6} (- 4 y^{7})$

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

$19 x^{1 - 12} y^{6} (- 4 y^{7})$

Subtract $12$ from $1$ .

$19 x^{- 11} y^{6} (- 4 y^{7})$

Step 2

Multiply $y^{6}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$19 x^{- 11} (y^{7} y^{6}) \cdot - 4$

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

$19 x^{- 11} y^{7 + 6} \cdot - 4$

Add $7$ and $6$ .

$19 x^{- 11} y^{13} \cdot - 4$

Step 3

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

$19 \frac{1}{x^{11}} y^{13} \cdot - 4$

Step 4

Combine $19$ and $\frac{1}{x^{11}}$ .

$\frac{19}{x^{11}} y^{13} \cdot - 4$

Step 5

Combine $\frac{19}{x^{11}}$ and $y^{13}$ .

$\frac{19 y^{13}}{x^{11}} \cdot - 4$

Step 6

Multiply $\frac{19 y^{13}}{x^{11}} \cdot - 4$ .

Combine $\frac{19 y^{13}}{x^{11}}$ and $- 4$ .

$\frac{19 y^{13} \cdot - 4}{x^{11}}$

Multiply $- 4$ by $19$ .

$\frac{- 76 y^{13}}{x^{11}}$

Step 7

Move the negative in front of the fraction.

$- \frac{76 y^{13}}{x^{11}}$