Simplify (m^-2n^4m^2)^-3

${(m^{- 2} n^{4} m^{2})}^{- 3}$

Step 1

Multiply $m^{- 2}$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

${(m^{2} m^{- 2} n^{4})}^{- 3}$

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

${(m^{2 - 2} n^{4})}^{- 3}$

Subtract $2$ from $2$ .

${(m^{0} n^{4})}^{- 3}$

Step 2

Simplify $m^{0} n^{4}$ .

${(n^{4})}^{- 3}$

Step 3

Multiply the exponents in ${(n^{4})}^{- 3}$ .

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

$n^{4 \cdot - 3}$

Multiply $4$ by $- 3$ .

$n^{- 12}$

Step 4

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

$\frac{1}{n^{12}}$