Simplify (3(y^-4)^4)/(12y^-6)

$\frac{3 {(y^{- 4})}^{4}}{12 y^{- 6}}$

Reduce the expression by cancelling the common factors.

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 {(y^{- 4})}^{4} y^{6}}{12}$

Cancel the common factor of $3$ and $12$ .

Factor $3$ out of $3 {(y^{- 4})}^{4} y^{6}$ .

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{3 \cdot 4}$

Cancel the common factor.

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{3 \cdot 4}$

Rewrite the expression.

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

Simplify the numerator.

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

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

$\frac{y^{- 4 \cdot 4} y^{6}}{4}$

Multiply $- 4$ by $4$ .

$\frac{y^{- 16} y^{6}}{4}$

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

$\frac{\frac{1}{y^{16}} y^{6}}{4}$

Simplify terms.

Combine $\frac{1}{y^{16}}$ and $y^{6}$ .

$\frac{\frac{y^{6}}{y^{16}}}{4}$

Reduce the expression $\frac{y^{6}}{y^{16}}$ by cancelling the common factors.

Multiply by $1$ .

$\frac{\frac{y^{6} \cdot 1}{y^{16}}}{4}$

Factor $y^{6}$ out of $y^{16}$ .

$\frac{\frac{y^{6} \cdot 1}{y^{6} y^{10}}}{4}$

Cancel the common factor.

$\frac{\frac{y^{6} \cdot 1}{y^{6} y^{10}}}{4}$

Rewrite the expression.

$\frac{\frac{1}{y^{10}}}{4}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{y^{10}} \cdot \frac{1}{4}$

Combine.

$\frac{1 \cdot 1}{y^{10} \cdot 4}$

Simplify the expression.

Multiply $1$ by $1$ .

$\frac{1}{y^{10} \cdot 4}$

Move $4$ to the left of $y^{10}$ .

$\frac{1}{4 y^{10}}$