Simplify (-a^3b^2c)^2

${(- a^{3} b^{2} c)}^{2}$

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

Apply the product rule to $- a^{3} b^{2} c$ .

${(- a^{3} b^{2})}^{2} c^{2}$

Apply the product rule to $- a^{3} b^{2}$ .

${(- a^{3})}^{2} {(b^{2})}^{2} c^{2}$

Apply the product rule to $- a^{3}$ .

${(- 1)}^{2} {(a^{3})}^{2} {(b^{2})}^{2} c^{2}$

Raise $- 1$ to the power of $2$ .

$1 {(a^{3})}^{2} {(b^{2})}^{2} c^{2}$

Multiply ${(a^{3})}^{2}$ by $1$ .

${(a^{3})}^{2} {(b^{2})}^{2} c^{2}$

Multiply the exponents in ${(a^{3})}^{2}$ .

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

$a^{3 \cdot 2} {(b^{2})}^{2} c^{2}$

Multiply $3$ by $2$ .

$a^{6} {(b^{2})}^{2} c^{2}$

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

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

$a^{6} b^{2 \cdot 2} c^{2}$

Multiply $2$ by $2$ .

$a^{6} b^{4} c^{2}$