Evaluate ((2m^2)^-1)/(m^2)

$\frac{{(2 m^{2})}^{- 1}}{m^{2}}$

Move ${(2 m^{2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{m^{2} (2 m^{2})}$

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

Move $m^{2}$ .

$\frac{1}{m^{2} m^{2} \cdot 2}$

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

$\frac{1}{m^{2 + 2} \cdot 2}$

Add $2$ and $2$ .

$\frac{1}{m^{4} \cdot 2}$

Move $2$ to the left of $m^{4}$ .

$\frac{1}{2 m^{4}}$