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

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

Step 1

Cancel the common factor of $y^{4}$ and $y^{3}$ .

Factor $y^{3}$ out of $2 y^{4}$ .

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

Cancel the common factors.

Multiply by $1$ .

${(\frac{y^{3} (2 y)}{y^{3} \cdot 1})}^{- 2}$

Cancel the common factor.

${(\frac{y^{3} (2 y)}{y^{3} \cdot 1})}^{- 2}$

Rewrite the expression.

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

Divide $2 y$ by $1$ .

${(2 y)}^{- 2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 y)}^{2}}$

Step 3

Simplify the denominator.

Apply the product rule to $2 y$ .

$\frac{1}{2^{2} y^{2}}$

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

$\frac{1}{4 y^{2}}$