Algebra Examples

$\sqrt[4]{p} \cdot \sqrt{p^{3}}$

Step 1

Factor out $p^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\sqrt[4]{p} \cdot (| p | \sqrt{p})$

Step 3

Multiply $\sqrt[4]{p} (| p | \sqrt{p})$ .

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Step 3.1

Rewrite the expression using the least common index of $4$ .

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Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{p}$ as $p^{\frac{1}{2}}$ .

$p^{\frac{1}{2}} \sqrt[4]{p} | p |$

Step 3.1.2

Rewrite $p^{\frac{1}{2}}$ as $p^{\frac{2}{4}}$ .

$p^{\frac{2}{4}} \sqrt[4]{p} | p |$

Step 3.1.3

Rewrite $p^{\frac{2}{4}}$ as $\sqrt[4]{p^{2}}$ .

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

Step 3.2

Combine using the product rule for radicals.

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

Step 3.3

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

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Step 3.3.1

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

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Step 3.3.1.1

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

$\sqrt[4]{p^{2} p^{1}} | p |$

Step 3.3.1.2

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

$\sqrt[4]{p^{2 + 1}} | p |$

Step 3.3.2

Add $2$ and $1$ .

$\sqrt[4]{p^{3}} | p |$