Simplify (5a^4)/(-2(a^4m^-4)^-1)

$\frac{5 a^{4}}{- 2 {(a^{4} m^{- 4})}^{- 1}}$

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

$\frac{5 a^{4} (a^{4} m^{- 4})}{- 2}$

Multiply $a^{4}$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$\frac{5 (a^{4} a^{4}) m^{- 4}}{- 2}$

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

$\frac{5 a^{4 + 4} m^{- 4}}{- 2}$

Add $4$ and $4$ .

$\frac{5 a^{8} m^{- 4}}{- 2}$

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

$\frac{5 a^{8}}{- 2 m^{4}}$

Move the negative in front of the fraction.

$- \frac{5 a^{8}}{2 m^{4}}$