Simplify -c(c^5)^2

$- c {(c^{5})}^{2}$

Multiply the exponents in ${(c^{5})}^{2}$ .

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

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

Multiply $5$ by $2$ .

$- c \cdot c^{10}$

Multiply $c$ by $c^{10}$ by adding the exponents.

Move $c^{10}$ .

$- (c^{10} c)$

Multiply $c^{10}$ by $c$ .

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

$- (c^{10} c^{1})$

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

$- c^{10 + 1}$

Add $10$ and $1$ .

$- c^{11}$