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

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

Step 1

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

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

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

Cancel the common factors.

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

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $y^{3}$ by $1$ .

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

Step 2

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

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

$y^{3 \cdot - 2}$

Multiply $3$ by $- 2$ .

$y^{- 6}$

Step 3

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

$\frac{1}{y^{6}}$