Simplify (2pq^2)^2(pq^2)^4

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

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

Apply the product rule to $2 p q^{2}$ .

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

Apply the product rule to $2 p$ .

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Apply the product rule to $p q^{2}$ .

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

Multiply $p^{2}$ by $p^{4}$ by adding the exponents.

Move $p^{4}$ .

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

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

$4 p^{4 + 2} q^{4} {(q^{2})}^{4}$

Add $4$ and $2$ .

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

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

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

$4 p^{6} q^{4} q^{2 \cdot 4}$

Multiply $2$ by $4$ .

$4 p^{6} q^{4} q^{8}$

Multiply $q^{4}$ by $q^{8}$ by adding the exponents.

Move $q^{8}$ .

$4 p^{6} (q^{8} q^{4})$

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

$4 p^{6} q^{8 + 4}$

Add $8$ and $4$ .

$4 p^{6} q^{12}$