Write the Fraction in Simplest Form (12m^2)/((4m)^-4)

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

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

$12 m^{2} {(4 m)}^{4}$

Apply the product rule to $4 m$ .

$12 m^{2} (4^{4} m^{4})$

Rewrite using the commutative property of multiplication.

$12 \cdot 4^{4} m^{2} m^{4}$

Multiply $m^{2}$ by $m^{4}$ by adding the exponents.

Move $m^{4}$ .

$12 \cdot 4^{4} (m^{4} m^{2})$

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

$12 \cdot 4^{4} m^{4 + 2}$

Add $4$ and $2$ .

$12 \cdot 4^{4} m^{6}$

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

$12 \cdot 256 m^{6}$

Multiply $12$ by $256$ .

$3072 m^{6}$