Simplify (19x^-6y^11)(-6xy^5)

$(19 x^{- 6} y^{11}) (- 6 x y^{5})$

Step 1

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

Move $x$ .

$19 (x \cdot x^{- 6}) y^{11} (- 6 y^{5})$

Multiply $x$ by $x^{- 6}$ .

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

$19 (x^{1} x^{- 6}) y^{11} (- 6 y^{5})$

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

$19 x^{1 - 6} y^{11} (- 6 y^{5})$

Subtract $6$ from $1$ .

$19 x^{- 5} y^{11} (- 6 y^{5})$

Step 2

Multiply $y^{11}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$19 x^{- 5} (y^{5} y^{11}) \cdot - 6$

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

$19 x^{- 5} y^{5 + 11} \cdot - 6$

Add $5$ and $11$ .

$19 x^{- 5} y^{16} \cdot - 6$

Step 3

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

$19 \frac{1}{x^{5}} y^{16} \cdot - 6$

Step 4

Combine $19$ and $\frac{1}{x^{5}}$ .

$\frac{19}{x^{5}} y^{16} \cdot - 6$

Step 5

Combine $\frac{19}{x^{5}}$ and $y^{16}$ .

$\frac{19 y^{16}}{x^{5}} \cdot - 6$

Step 6

Multiply $\frac{19 y^{16}}{x^{5}} \cdot - 6$ .

Combine $\frac{19 y^{16}}{x^{5}}$ and $- 6$ .

$\frac{19 y^{16} \cdot - 6}{x^{5}}$

Multiply $- 6$ by $19$ .

$\frac{- 114 y^{16}}{x^{5}}$

Step 7

Move the negative in front of the fraction.

$- \frac{114 y^{16}}{x^{5}}$