Find the Product (3p^4)^3*(p^2)^7

${(3 p^{4})}^{3} \cdot {(p^{2})}^{7}$

Apply the product rule to $3 p^{4}$ .

$3^{3} {(p^{4})}^{3} \cdot {(p^{2})}^{7}$

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

$27 {(p^{4})}^{3} \cdot {(p^{2})}^{7}$

Multiply the exponents in ${(p^{4})}^{3}$ .

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

$27 p^{4 \cdot 3} \cdot {(p^{2})}^{7}$

Multiply $4$ by $3$ .

$27 p^{12} \cdot {(p^{2})}^{7}$

Multiply the exponents in ${(p^{2})}^{7}$ .

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

$27 p^{12} \cdot p^{2 \cdot 7}$

Multiply $2$ by $7$ .

$27 p^{12} \cdot p^{14}$

Multiply $p^{12}$ by $p^{14}$ by adding the exponents.

Move $p^{14}$ .

$27 (p^{14} p^{12})$

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

$27 p^{14 + 12}$

Add $14$ and $12$ .

$27 p^{26}$