Simplify ((-4y^2)^4)/(-12y^-2)

$\frac{{(- 4 y^{2})}^{4}}{- 12 y^{- 2}}$

Step 1

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

$\frac{{(- 4 y^{2})}^{4} y^{2}}{- 12}$

Step 2

Simplify the numerator.

Apply the product rule to $- 4 y^{2}$ .

$\frac{{(- 4)}^{4} {(y^{2})}^{4} y^{2}}{- 12}$

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

$\frac{256 {(y^{2})}^{4} y^{2}}{- 12}$

Multiply the exponents in ${(y^{2})}^{4}$ .

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

$\frac{256 y^{2 \cdot 4} y^{2}}{- 12}$

Multiply $2$ by $4$ .

$\frac{256 y^{8} y^{2}}{- 12}$

Multiply $y^{8}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{256 (y^{2} y^{8})}{- 12}$

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

$\frac{256 y^{2 + 8}}{- 12}$

Add $2$ and $8$ .

$\frac{256 y^{10}}{- 12}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $256$ and $- 12$ .

Factor $4$ out of $256 y^{10}$ .

$\frac{4 (64 y^{10})}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$\frac{4 (64 y^{10})}{4 (- 3)}$

Cancel the common factor.

$\frac{4 (64 y^{10})}{4 \cdot - 3}$

Rewrite the expression.

$\frac{64 y^{10}}{- 3}$

Move the negative in front of the fraction.

$- \frac{64 y^{10}}{3}$