Simplify the Radical Expression fourth root of p* square root of p^3

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

Factor out $p^{2}$ .

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

Pull terms out from under the radical.

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

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

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

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

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

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

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

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

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

Add $2$ and $1$ .

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