Simplify ((2x^-2y^7)/(6xy^-1))^-2

${(\frac{2 x^{- 2} y^{7}}{6 x y^{- 1}})}^{- 2}$

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

${(\frac{2 y^{7}}{6 x y^{- 1} x^{2}})}^{- 2}$

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

Move $x^{2}$ .

${(\frac{2 y^{7}}{6 (x^{2} x) y^{- 1}})}^{- 2}$

Multiply $x^{2}$ by $x$ .

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

${(\frac{2 y^{7}}{6 (x^{2} x^{1}) y^{- 1}})}^{- 2}$

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

${(\frac{2 y^{7}}{6 x^{2 + 1} y^{- 1}})}^{- 2}$

Add $2$ and $1$ .

${(\frac{2 y^{7}}{6 x^{3} y^{- 1}})}^{- 2}$

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

${(\frac{2 y^{7} y}{6 x^{3}})}^{- 2}$

Multiply $y^{7}$ by $y$ by adding the exponents.

Move $y$ .

${(\frac{2 (y \cdot y^{7})}{6 x^{3}})}^{- 2}$

Multiply $y$ by $y^{7}$ .

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

${(\frac{2 (y^{1} y^{7})}{6 x^{3}})}^{- 2}$

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

${(\frac{2 y^{1 + 7}}{6 x^{3}})}^{- 2}$

Add $1$ and $7$ .

${(\frac{2 y^{8}}{6 x^{3}})}^{- 2}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 y^{8}$ .

${(\frac{2 (y^{8})}{6 x^{3}})}^{- 2}$

Cancel the common factors.

Factor $2$ out of $6 x^{3}$ .

${(\frac{2 (y^{8})}{2 (3 x^{3})})}^{- 2}$

Cancel the common factor.

${(\frac{2 y^{8}}{2 (3 x^{3})})}^{- 2}$

Rewrite the expression.

${(\frac{y^{8}}{3 x^{3}})}^{- 2}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{3 x^{3}}{y^{8}})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 x^{3}}{y^{8}}$ .

$\frac{{(3 x^{3})}^{2}}{{(y^{8})}^{2}}$

Apply the product rule to $3 x^{3}$ .

$\frac{3^{2} {(x^{3})}^{2}}{{(y^{8})}^{2}}$

Simplify the numerator.

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

$\frac{9 {(x^{3})}^{2}}{{(y^{8})}^{2}}$

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$\frac{9 x^{3 \cdot 2}}{{(y^{8})}^{2}}$

Multiply $3$ by $2$ .

$\frac{9 x^{6}}{{(y^{8})}^{2}}$

Multiply the exponents in ${(y^{8})}^{2}$ .

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

$\frac{9 x^{6}}{y^{8 \cdot 2}}$

Multiply $8$ by $2$ .

$\frac{9 x^{6}}{y^{16}}$

Simplify ((2x^-2y^7)/(6xy^-1))^-2

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