Simplify (17x^-9y^9)(-9xy^9)

$(17 x^{- 9} y^{9}) (- 9 x y^{9})$

Step 1

Multiply $x^{- 9}$ by $x$ by adding the exponents.

Move $x$ .

$17 (x \cdot x^{- 9}) y^{9} (- 9 y^{9})$

Multiply $x$ by $x^{- 9}$ .

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

$17 (x^{1} x^{- 9}) y^{9} (- 9 y^{9})$

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

$17 x^{1 - 9} y^{9} (- 9 y^{9})$

Subtract $9$ from $1$ .

$17 x^{- 8} y^{9} (- 9 y^{9})$

Step 2

Multiply $y^{9}$ by $y^{9}$ by adding the exponents.

Move $y^{9}$ .

$17 x^{- 8} (y^{9} y^{9}) \cdot - 9$

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

$17 x^{- 8} y^{9 + 9} \cdot - 9$

Add $9$ and $9$ .

$17 x^{- 8} y^{18} \cdot - 9$

Step 3

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

$17 \frac{1}{x^{8}} y^{18} \cdot - 9$

Step 4

Combine $17$ and $\frac{1}{x^{8}}$ .

$\frac{17}{x^{8}} y^{18} \cdot - 9$

Step 5

Combine $\frac{17}{x^{8}}$ and $y^{18}$ .

$\frac{17 y^{18}}{x^{8}} \cdot - 9$

Step 6

Multiply $\frac{17 y^{18}}{x^{8}} \cdot - 9$ .

Combine $\frac{17 y^{18}}{x^{8}}$ and $- 9$ .

$\frac{17 y^{18} \cdot - 9}{x^{8}}$

Multiply $- 9$ by $17$ .

$\frac{- 153 y^{18}}{x^{8}}$

Step 7

Move the negative in front of the fraction.

$- \frac{153 y^{18}}{x^{8}}$