Simplify (-4(m^-3z^4)^2)/(12m^-4z^-1)

$\frac{- 4 {(m^{- 3} z^{4})}^{2}}{12 m^{- 4} z^{- 1}}$

Reduce the expression by cancelling the common factors.

Move $m^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 4 {(m^{- 3} z^{4})}^{2} m^{4}}{12 z^{- 1}}$

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

$\frac{- 4 {(m^{- 3} z^{4})}^{2} m^{4} z}{12}$

Cancel the common factor of $- 4$ and $12$ .

Factor $4$ out of $- 4 {(m^{- 3} z^{4})}^{2} m^{4} z$ .

$\frac{4 (- {(m^{- 3} z^{4})}^{2} m^{4} z)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

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

Cancel the common factor.

$\frac{4 (- {(m^{- 3} z^{4})}^{2} m^{4} z)}{4 \cdot 3}$

Rewrite the expression.

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

Simplify the numerator.

Apply the product rule to $m^{- 3} z^{4}$ .

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

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

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

$\frac{- m^{- 3 \cdot 2} {(z^{4})}^{2} m^{4} z}{3}$

Multiply $- 3$ by $2$ .

$\frac{- m^{- 6} {(z^{4})}^{2} m^{4} z}{3}$

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

$\frac{- \frac{1}{m^{6}} {(z^{4})}^{2} m^{4} z}{3}$

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

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

$\frac{- \frac{1}{m^{6}} z^{4 \cdot 2} m^{4} z}{3}$

Multiply $4$ by $2$ .

$\frac{- \frac{1}{m^{6}} z^{8} m^{4} z}{3}$

Combine exponents.

Combine $z^{8}$ and $\frac{1}{m^{6}}$ .

$\frac{- \frac{z^{8}}{m^{6}} m^{4} z}{3}$

Combine $m^{4}$ and $\frac{z^{8}}{m^{6}}$ .

$\frac{- \frac{m^{4} z^{8}}{m^{6}} z}{3}$

Combine $z$ and $\frac{m^{4} z^{8}}{m^{6}}$ .

$\frac{- \frac{z (m^{4} z^{8})}{m^{6}}}{3}$

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

$\frac{- \frac{m^{4} (z^{1} z^{8})}{m^{6}}}{3}$

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

$\frac{- \frac{m^{4} z^{1 + 8}}{m^{6}}}{3}$

Add $1$ and $8$ .

$\frac{- \frac{m^{4} z^{9}}{m^{6}}}{3}$

Reduce the expression $\frac{m^{4} z^{9}}{m^{6}}$ by cancelling the common factors.

Factor $m^{4}$ out of $m^{4} z^{9}$ .

$\frac{- \frac{m^{4} (z^{9})}{m^{6}}}{3}$

Factor $m^{4}$ out of $m^{6}$ .

$\frac{- \frac{m^{4} (z^{9})}{m^{4} m^{2}}}{3}$

Cancel the common factor.

$\frac{- \frac{m^{4} z^{9}}{m^{4} m^{2}}}{3}$

Rewrite the expression.

$\frac{- \frac{z^{9}}{m^{2}}}{3}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{z^{9}}{m^{2}} \cdot \frac{1}{3}$

Multiply $\frac{1}{3}$ by $\frac{z^{9}}{m^{2}}$ .

$- \frac{z^{9}}{3 m^{2}}$

Simplify (-4(m^-3z^4)^2)/(12m^-4z^-1)

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