Simplify (12x^-5y^3)/(3^-2x^-2y^-4)

$\frac{12 x^{- 5} y^{3}}{3^{- 2} x^{- 2} y^{- 4}}$

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

$\frac{12 y^{3}}{3^{- 2} x^{- 2} y^{- 4} x^{5}}$

Multiply $x^{- 2}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{12 y^{3}}{3^{- 2} (x^{5} x^{- 2}) y^{- 4}}$

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

$\frac{12 y^{3}}{3^{- 2} x^{5 - 2} y^{- 4}}$

Subtract $2$ from $5$ .

$\frac{12 y^{3}}{3^{- 2} x^{3} y^{- 4}}$

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

$\frac{12 y^{3} y^{4}}{3^{- 2} x^{3}}$

Move $3^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 y^{3} y^{4} \cdot 3^{2}}{x^{3}}$

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

Move $y^{4}$ .

$\frac{12 (y^{4} y^{3}) \cdot 3^{2}}{x^{3}}$

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

$\frac{12 y^{4 + 3} \cdot 3^{2}}{x^{3}}$

Add $4$ and $3$ .

$\frac{12 y^{7} \cdot 3^{2}}{x^{3}}$

Simplify the numerator.

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

$\frac{12 y^{7} \cdot 9}{x^{3}}$

Multiply $9$ by $12$ .

$\frac{108 y^{7}}{x^{3}}$