Simplify (3pq^4)^2(6p^6q)^2

${(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$

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

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

${(3 p)}^{2} {(q^{4})}^{2} {(6 p^{6} q)}^{2}$

Apply the product rule to $3 p$ .

$3^{2} p^{2} {(q^{4})}^{2} {(6 p^{6} q)}^{2}$

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

$9 p^{2} {(q^{4})}^{2} {(6 p^{6} q)}^{2}$

Multiply the exponents in ${(q^{4})}^{2}$ .

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

$9 p^{2} q^{4 \cdot 2} {(6 p^{6} q)}^{2}$

Multiply $4$ by $2$ .

$9 p^{2} q^{8} {(6 p^{6} q)}^{2}$

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

Apply the product rule to $6 p^{6} q$ .

$9 p^{2} q^{8} ({(6 p^{6})}^{2} q^{2})$

Apply the product rule to $6 p^{6}$ .

$9 p^{2} q^{8} (6^{2} {(p^{6})}^{2} q^{2})$

Multiply $q^{8}$ by $q^{2}$ by adding the exponents.

Move $q^{2}$ .

$9 p^{2} (q^{2} q^{8}) (6^{2} {(p^{6})}^{2})$

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

$9 p^{2} q^{2 + 8} (6^{2} {(p^{6})}^{2})$

Add $2$ and $8$ .

$9 p^{2} q^{10} (6^{2} {(p^{6})}^{2})$

Raise $6$ to the power of $2$ .

$9 p^{2} q^{10} (36 {(p^{6})}^{2})$

Multiply the exponents in ${(p^{6})}^{2}$ .

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

$9 p^{2} q^{10} (36 p^{6 \cdot 2})$

Multiply $6$ by $2$ .

$9 p^{2} q^{10} (36 p^{12})$

Multiply $p^{2}$ by $p^{12}$ by adding the exponents.

Move $p^{12}$ .

$9 (p^{12} p^{2}) q^{10} \cdot 36$

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

$9 p^{12 + 2} q^{10} \cdot 36$

Add $12$ and $2$ .

$9 p^{14} q^{10} \cdot 36$

Multiply $36$ by $9$ .

$324 p^{14} q^{10}$