Simplify 2 fourth root of p^2q*7 fourth root of p^3q^10

$2 \sqrt[4]{p^{2} q} \cdot 7 \sqrt[4]{p^{3} q^{10}}$

Rewrite $p^{3} q^{10}$ as ${(q^{2})}^{4} (p^{3} q^{2})$ .

Factor out $q^{8}$ .

$2 \sqrt[4]{p^{2} q} \cdot (7 \sqrt[4]{p^{3} (q^{8} q^{2})})$

Rewrite $q^{8}$ as ${(q^{2})}^{4}$ .

$2 \sqrt[4]{p^{2} q} \cdot (7 \sqrt[4]{p^{3} ({(q^{2})}^{4} q^{2})})$

Reorder $p^{3}$ and ${(q^{2})}^{4}$ .

$2 \sqrt[4]{p^{2} q} \cdot (7 \sqrt[4]{{(q^{2})}^{4} p^{3} q^{2}})$

Add parentheses.

$2 \sqrt[4]{p^{2} q} \cdot (7 \sqrt[4]{{(q^{2})}^{4} (p^{3} q^{2})})$

Pull terms out from under the radical.

$2 \sqrt[4]{p^{2} q} \cdot (7 (q^{2} \sqrt[4]{p^{3} q^{2}}))$

Multiply $2 \sqrt[4]{p^{2} q} (7 q^{2} \sqrt[4]{p^{3} q^{2}})$ .

Multiply $7$ by $2$ .

$14 \sqrt[4]{p^{2} q} (q^{2} \sqrt[4]{p^{3} q^{2}})$

Combine using the product rule for radicals.

$14 (q^{2} \sqrt[4]{p^{2} q (p^{3} q^{2})})$

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

$14 (q^{2} \sqrt[4]{p^{3 + 2} q \cdot q^{2}})$

Add $3$ and $2$ .

$14 (q^{2} \sqrt[4]{p^{5} q \cdot q^{2}})$

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

Move $q^{2}$ .

$14 (q^{2} \sqrt[4]{p^{5} (q^{2} q)})$

Multiply $q^{2}$ by $q$ .

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

$14 (q^{2} \sqrt[4]{p^{5} (q^{2} q^{1})})$

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

$14 (q^{2} \sqrt[4]{p^{5} q^{2 + 1}})$

Add $2$ and $1$ .

$14 (q^{2} \sqrt[4]{p^{5} q^{3}})$

Rewrite $p^{5} q^{3}$ as $p^{4} (p q^{3})$ .

Factor out $p^{4}$ .

$14 (q^{2} \sqrt[4]{p^{4} p q^{3}})$

Add parentheses.

$14 (q^{2} \sqrt[4]{p^{4} (p q^{3})})$

Pull terms out from under the radical.

$14 (q^{2} (p \sqrt[4]{p q^{3}}))$

Reorder factors in $14 q^{2} (p \sqrt[4]{p q^{3}})$ .

$14 q^{2} p \sqrt[4]{p q^{3}}$