Simplify (-9x^-1y^-9)/(-15x^5y^-3)

$\frac{- 9 x^{- 1} y^{- 9}}{- 15 x^{5} y^{- 3}}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 9 y^{- 9}}{- 15 x^{5} y^{- 3} x}$

Step 2

Move $y^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 9}{- 15 x^{5} y^{- 3} x y^{9}}$

Step 3

Simplify the denominator.

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{- 9}{- 15 (x \cdot x^{5}) y^{- 3} y^{9}}$

Multiply $x$ by $x^{5}$ .

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

$\frac{- 9}{- 15 (x^{1} x^{5}) y^{- 3} y^{9}}$

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

$\frac{- 9}{- 15 x^{1 + 5} y^{- 3} y^{9}}$

Add $1$ and $5$ .

$\frac{- 9}{- 15 x^{6} y^{- 3} y^{9}}$

Multiply $y^{- 3}$ by $y^{9}$ by adding the exponents.

Move $y^{9}$ .

$\frac{- 9}{- 15 x^{6} (y^{9} y^{- 3})}$

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

$\frac{- 9}{- 15 x^{6} y^{9 - 3}}$

Subtract $3$ from $9$ .

$\frac{- 9}{- 15 x^{6} y^{6}}$

Step 4

Cancel the common factor of $- 9$ and $- 15$ .

Factor $- 3$ out of $- 9$ .

$\frac{- 3 (3)}{- 15 x^{6} y^{6}}$

Cancel the common factors.

Factor $- 3$ out of $- 15 x^{6} y^{6}$ .

$\frac{- 3 (3)}{- 3 (5 x^{6} y^{6})}$

Cancel the common factor.

$\frac{- 3 \cdot 3}{- 3 (5 x^{6} y^{6})}$

Rewrite the expression.

$\frac{3}{5 x^{6} y^{6}}$