Simplify -c(c^4)^2

$- c {(c^{4})}^{2}$

Multiply the exponents in ${(c^{4})}^{2}$ .

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

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

Multiply $4$ by $2$ .

$- c \cdot c^{8}$

Multiply $c$ by $c^{8}$ by adding the exponents.

Move $c^{8}$ .

$- (c^{8} c)$

Multiply $c^{8}$ by $c$ .

Raise $c$ to the power of $1$ .

$- (c^{8} c^{1})$

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

$- c^{8 + 1}$

Add $8$ and $1$ .

$- c^{9}$