Simplify (3^-2x^-3y^4)/(6^-2x^-2y^-2)

$\frac{3^{- 2} x^{- 3} y^{4}}{6^{- 2} x^{- 2} y^{- 2}}$

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

$\frac{x^{- 3} y^{4}}{6^{- 2} x^{- 2} y^{- 2} \cdot 3^{2}}$

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

$\frac{y^{4}}{6^{- 2} x^{- 2} y^{- 2} \cdot 3^{2} x^{3}}$

Simplify the denominator.

Multiply $x^{- 2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{y^{4}}{6^{- 2} (x^{3} x^{- 2}) y^{- 2} \cdot 3^{2}}$

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

$\frac{y^{4}}{6^{- 2} x^{3 - 2} y^{- 2} \cdot 3^{2}}$

Subtract $2$ from $3$ .

$\frac{y^{4}}{6^{- 2} x^{1} y^{- 2} \cdot 3^{2}}$

Simplify $6^{- 2} x^{1} y^{- 2} \cdot 3^{2}$ .

$\frac{y^{4}}{6^{- 2} x y^{- 2} \cdot 3^{2}}$

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

$\frac{y^{4} y^{2}}{6^{- 2} x \cdot 3^{2}}$

Move $6^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{4} y^{2} \cdot 6^{2}}{x \cdot 3^{2}}$

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

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

$\frac{y^{4 + 2} \cdot 6^{2}}{x \cdot 3^{2}}$

Add $4$ and $2$ .

$\frac{y^{6} \cdot 6^{2}}{x \cdot 3^{2}}$

Evaluate the exponents.

Raise $6$ to the power of $2$ .

$\frac{y^{6} \cdot 36}{x \cdot 3^{2}}$

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

$\frac{y^{6} \cdot 36}{x \cdot 9}$

Cancel the common factor of $36$ and $9$ .

Factor $9$ out of $y^{6} \cdot 36$ .

$\frac{9 (y^{6} \cdot 4)}{x \cdot 9}$

Cancel the common factors.

Factor $9$ out of $x \cdot 9$ .

$\frac{9 (y^{6} \cdot 4)}{9 \cdot x}$

Cancel the common factor.

$\frac{9 (y^{6} \cdot 4)}{9 \cdot x}$

Rewrite the expression.

$\frac{y^{6} \cdot 4}{x}$

Move $4$ to the left of $y^{6}$ .

$\frac{4 y^{6}}{x}$