Simplify (-5c^-2)/(-4(c^4)^4)

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

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

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

Simplify the denominator.

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

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

$\frac{- 5}{- 4 c^{4 \cdot 4} c^{2}}$

Multiply $4$ by $4$ .

$\frac{- 5}{- 4 c^{16} c^{2}}$

Multiply $c^{16}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

$\frac{- 5}{- 4 (c^{2} c^{16})}$

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

$\frac{- 5}{- 4 c^{2 + 16}}$

Add $2$ and $16$ .

$\frac{- 5}{- 4 c^{18}}$

Dividing two negative values results in a positive value.

$\frac{5}{4 c^{18}}$