Simplify ((10y^4)/(4y^6))^-2

${(\frac{10 y^{4}}{4 y^{6}})}^{- 2}$

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10 y^{4}$ .

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

Cancel the common factors.

Factor $2$ out of $4 y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{4}$ and $y^{6}$ .

Factor $y^{4}$ out of $5 y^{4}$ .

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

Cancel the common factors.

Factor $y^{4}$ out of $2 y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

${(\frac{2 y^{2}}{5})}^{2}$

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

Apply the product rule to $\frac{2 y^{2}}{5}$ .

$\frac{{(2 y^{2})}^{2}}{5^{2}}$

Apply the product rule to $2 y^{2}$ .

$\frac{2^{2} {(y^{2})}^{2}}{5^{2}}$

Simplify the numerator.

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

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

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

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

$\frac{4 y^{2 \cdot 2}}{5^{2}}$

Multiply $2$ by $2$ .

$\frac{4 y^{4}}{5^{2}}$

Raise $5$ to the power of $2$ .

$\frac{4 y^{4}}{25}$