Simplify ((6x^-2y^2)^-1)/((6^4x^4y^5)^-4)

$\frac{{(6 x^{- 2} y^{2})}^{- 1}}{{(6^{4} x^{4} y^{5})}^{- 4}}$

Simplify the expression.

Move ${(6 x^{- 2} y^{2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(6^{4} x^{4} y^{5})}^{- 4} (6 x^{- 2} y^{2})}$

Move ${(6^{4} x^{4} y^{5})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(6^{4} x^{4} y^{5})}^{4}}{6 x^{- 2} y^{2}}$

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

$\frac{{(6^{4} x^{4} y^{5})}^{4} x^{2}}{6 y^{2}}$

Simplify the numerator.

Apply the product rule to $6^{4} x^{4} y^{5}$ .

$\frac{{(6^{4} x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Raise $6$ to the power of $4$ .

$\frac{{(1296 x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Apply the product rule to $1296 x^{4}$ .

$\frac{1296^{4} {(x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Raise $1296$ to the power of $4$ .

$\frac{2821109907456 {(x^{4})}^{4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Multiply the exponents in ${(x^{4})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2821109907456 x^{4 \cdot 4} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Multiply $4$ by $4$ .

$\frac{2821109907456 x^{16} {(y^{5})}^{4} x^{2}}{6 y^{2}}$

Multiply the exponents in ${(y^{5})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2821109907456 x^{16} y^{5 \cdot 4} x^{2}}{6 y^{2}}$

Multiply $5$ by $4$ .

$\frac{2821109907456 x^{16} y^{20} x^{2}}{6 y^{2}}$

Multiply $x^{16}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{2821109907456 (x^{2} x^{16}) y^{20}}{6 y^{2}}$

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

$\frac{2821109907456 x^{2 + 16} y^{20}}{6 y^{2}}$

Add $2$ and $16$ .

$\frac{2821109907456 x^{18} y^{20}}{6 y^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2821109907456$ and $6$ .

Factor $6$ out of $2821109907456 x^{18} y^{20}$ .

$\frac{6 (470184984576 x^{18} y^{20})}{6 y^{2}}$

Cancel the common factors.

Factor $6$ out of $6 y^{2}$ .

$\frac{6 (470184984576 x^{18} y^{20})}{6 (y^{2})}$

Cancel the common factor.

$\frac{6 (470184984576 x^{18} y^{20})}{6 y^{2}}$

Rewrite the expression.

$\frac{470184984576 x^{18} y^{20}}{y^{2}}$

Cancel the common factor of $y^{20}$ and $y^{2}$ .

Factor $y^{2}$ out of $470184984576 x^{18} y^{20}$ .

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2} \cdot 1}$

Cancel the common factor.

$\frac{y^{2} (470184984576 x^{18} y^{18})}{y^{2} \cdot 1}$

Rewrite the expression.

$\frac{470184984576 x^{18} y^{18}}{1}$

Divide $470184984576 x^{18} y^{18}$ by $1$ .

$470184984576 x^{18} y^{18}$

Simplify ((6x^-2y^2)^-1)/((6^4x^4y^5)^-4)

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