Simplify 3cd(2c^12d^15)^3

$3 c d {(2 c^{12} d^{15})}^{3}$

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

Apply the product rule to $2 c^{12} d^{15}$ .

$3 c d ({(2 c^{12})}^{3} {(d^{15})}^{3})$

Apply the product rule to $2 c^{12}$ .

$3 c d (2^{3} {(c^{12})}^{3} {(d^{15})}^{3})$

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

$3 c d (8 {(c^{12})}^{3} {(d^{15})}^{3})$

Multiply the exponents in ${(c^{12})}^{3}$ .

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

$3 c d (8 c^{12 \cdot 3} {(d^{15})}^{3})$

Multiply $12$ by $3$ .

$3 c d (8 c^{36} {(d^{15})}^{3})$

Multiply $c$ by $c^{36}$ by adding the exponents.

Move $c^{36}$ .

$3 (c^{36} c) d (8 {(d^{15})}^{3})$

Multiply $c^{36}$ by $c$ .

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

$3 (c^{36} c^{1}) d (8 {(d^{15})}^{3})$

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

$3 c^{36 + 1} d (8 {(d^{15})}^{3})$

Add $36$ and $1$ .

$3 c^{37} d (8 {(d^{15})}^{3})$

Multiply the exponents in ${(d^{15})}^{3}$ .

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

$3 c^{37} d (8 d^{15 \cdot 3})$

Multiply $15$ by $3$ .

$3 c^{37} d (8 d^{45})$

Multiply $d$ by $d^{45}$ by adding the exponents.

Move $d^{45}$ .

$3 c^{37} (d^{45} d) \cdot 8$

Multiply $d^{45}$ by $d$ .

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

$3 c^{37} (d^{45} d^{1}) \cdot 8$

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

$3 c^{37} d^{45 + 1} \cdot 8$

Add $45$ and $1$ .

$3 c^{37} d^{46} \cdot 8$

Multiply $8$ by $3$ .

$24 c^{37} d^{46}$