Simplify 36c^5d^3(cd^2)^3

$36 c^{5} d^{3} {(c d^{2})}^{3}$

Apply the product rule to $c d^{2}$ .

$36 c^{5} d^{3} (c^{3} {(d^{2})}^{3})$

Multiply $c^{5}$ by $c^{3}$ by adding the exponents.

Move $c^{3}$ .

$36 (c^{3} c^{5}) d^{3} {(d^{2})}^{3}$

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

$36 c^{3 + 5} d^{3} {(d^{2})}^{3}$

Add $3$ and $5$ .

$36 c^{8} d^{3} {(d^{2})}^{3}$

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

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

$36 c^{8} d^{3} d^{2 \cdot 3}$

Multiply $2$ by $3$ .

$36 c^{8} d^{3} d^{6}$

Multiply $d^{3}$ by $d^{6}$ by adding the exponents.

Move $d^{6}$ .

$36 c^{8} (d^{6} d^{3})$

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

$36 c^{8} d^{6 + 3}$

Add $6$ and $3$ .

$36 c^{8} d^{9}$