Simplify (-12y^-8)/((-3y^-1)^4)

$\frac{- 12 y^{- 8}}{{(- 3 y^{- 1})}^{4}}$

Move $y^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 12}{{(- 3 y^{- 1})}^{4} y^{8}}$

Simplify the denominator.

Apply the product rule to $- 3 y^{- 1}$ .

$\frac{- 12}{{(- 3)}^{4} {(y^{- 1})}^{4} y^{8}}$

Raise $- 3$ to the power of $4$ .

$\frac{- 12}{81 {(y^{- 1})}^{4} y^{8}}$

Multiply the exponents in ${(y^{- 1})}^{4}$ .

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

$\frac{- 12}{81 y^{- 1 \cdot 4} y^{8}}$

Multiply $- 1$ by $4$ .

$\frac{- 12}{81 y^{- 4} y^{8}}$

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

$\frac{- 12}{81 \frac{1}{y^{4}} y^{8}}$

Combine exponents.

Combine $81$ and $\frac{1}{y^{4}}$ .

$\frac{- 12}{\frac{81}{y^{4}} y^{8}}$

Combine $\frac{81}{y^{4}}$ and $y^{8}$ .

$\frac{- 12}{\frac{81 y^{8}}{y^{4}}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{81 y^{8}}{y^{4}}$ by cancelling the common factors.

Factor $y^{4}$ out of $81 y^{8}$ .

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4}}}$

Multiply by $1$ .

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4} \cdot 1}}$

Cancel the common factor.

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4} \cdot 1}}$

Rewrite the expression.

$\frac{- 12}{\frac{81 y^{4}}{1}}$

Divide $81 y^{4}$ by $1$ .

$\frac{- 12}{81 y^{4}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 12$ and $81$ .

Factor $3$ out of $- 12$ .

$\frac{3 (- 4)}{81 y^{4}}$

Cancel the common factors.

Factor $3$ out of $81 y^{4}$ .

$\frac{3 (- 4)}{3 (27 y^{4})}$

Cancel the common factor.

$\frac{3 \cdot - 4}{3 (27 y^{4})}$

Rewrite the expression.

$\frac{- 4}{27 y^{4}}$

Move the negative in front of the fraction.

$- \frac{4}{27 y^{4}}$