Basic Math Examples

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

Step 1

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

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $q^{3}$ by $q^{3}$ by adding the exponents.

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Step 1.2.1

Move $q^{3}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Add $3$ and $3$ .

$p \sqrt[4]{p^{2} q^{6}}$

Step 2

Rewrite $p^{2} q^{6}$ as $q^{4} (p^{2} q^{2})$ .

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Step 2.1

Factor out $q^{4}$ .

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

Step 2.2

Reorder $p^{2}$ and $q^{4}$ .

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

Step 2.3

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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

Step 5

Rewrite $\sqrt[4]{{(p q)}^{2}}$ as $\sqrt{\sqrt{{(p q)}^{2}}}$ .

$p (q \sqrt{\sqrt{{(p q)}^{2}}})$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$p (q \sqrt{p q})$

Step 7

Reorder factors in $p (q \sqrt{p q})$ .

$p q \sqrt{p q}$