Simplify -(-cb^7)^3

$- {(- c b^{7})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- c b^{7}$ .

$- ({(- c)}^{3} {(b^{7})}^{3})$

Apply the product rule to $- c$ .

$- ({(- 1)}^{3} c^{3} {(b^{7})}^{3})$

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Move ${(- 1)}^{3}$ .

${(- 1)}^{3} \cdot - 1 (c^{3} {(b^{7})}^{3})$

Multiply ${(- 1)}^{3}$ by $- 1$ .

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

${(- 1)}^{3} \cdot {(- 1)}^{1} (c^{3} {(b^{7})}^{3})$

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

${(- 1)}^{3 + 1} (c^{3} {(b^{7})}^{3})$

Add $3$ and $1$ .

${(- 1)}^{4} (c^{3} {(b^{7})}^{3})$

Raise $- 1$ to the power of $4$ .

$1 (c^{3} {(b^{7})}^{3})$

Multiply $c^{3} {(b^{7})}^{3}$ by $1$ .

$c^{3} {(b^{7})}^{3}$

Multiply the exponents in ${(b^{7})}^{3}$ .

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

$c^{3} b^{7 \cdot 3}$

Multiply $7$ by $3$ .

$c^{3} b^{21}$