Simplify (c^3)^2(-3c^5)^2

${(c^{3})}^{2} {(- 3 c^{5})}^{2}$

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

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

$c^{3 \cdot 2} {(- 3 c^{5})}^{2}$

Multiply $3$ by $2$ .

$c^{6} {(- 3 c^{5})}^{2}$

Apply the product rule to $- 3 c^{5}$ .

$c^{6} ({(- 3)}^{2} {(c^{5})}^{2})$

Rewrite using the commutative property of multiplication.

${(- 3)}^{2} c^{6} {(c^{5})}^{2}$

Raise $- 3$ to the power of $2$ .

$9 c^{6} {(c^{5})}^{2}$

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

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

$9 c^{6} c^{5 \cdot 2}$

Multiply $5$ by $2$ .

$9 c^{6} c^{10}$

Multiply $c^{6}$ by $c^{10}$ by adding the exponents.

Move $c^{10}$ .

$9 (c^{10} c^{6})$

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

$9 c^{10 + 6}$

Add $10$ and $6$ .

$9 c^{16}$