Simplify (3^2x^-3y^-4)/(2^-1x^-4y^-5)

$\frac{3^{2} x^{- 3} y^{- 4}}{2^{- 1} x^{- 4} y^{- 5}}$

Step 1

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{2} x^{- 3} y^{- 4} x^{4}}{2^{- 1} y^{- 5}}$

Step 2

Move $y^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{2} x^{- 3} y^{- 4} x^{4} y^{5}}{2^{- 1}}$

Step 3

Move $2^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{2} x^{- 3} y^{- 4} x^{4} y^{5} \cdot 2$

Step 4

Multiply $x^{- 3}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$3^{2} (x^{4} x^{- 3}) y^{- 4} y^{5} \cdot 2$

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

$3^{2} x^{4 - 3} y^{- 4} y^{5} \cdot 2$

Subtract $3$ from $4$ .

$3^{2} x^{1} y^{- 4} y^{5} \cdot 2$

Step 5

Simplify $3^{2} x^{1} y^{- 4}$ .

$3^{2} x y^{- 4} y^{5} \cdot 2$

Step 6

Multiply $y^{- 4}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$3^{2} x (y^{5} y^{- 4}) \cdot 2$

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

$3^{2} x y^{5 - 4} \cdot 2$

Subtract $4$ from $5$ .

$3^{2} x y^{1} \cdot 2$

Step 7

Simplify $3^{2} x y^{1}$ .

$3^{2} x y \cdot 2$

Step 8

Raise $3$ to the power of $2$ .

$9 x y \cdot 2$

Step 9

Multiply $2$ by $9$ .

$18 x y$