Simplify square root of p^3 cube root of p^11

$\sqrt{p^{3}} \sqrt[3]{p^{11}}$

Factor out $p^{2}$ .

$\sqrt{p^{2} p} \sqrt[3]{p^{11}}$

Pull terms out from under the radical.

$p \sqrt{p} \sqrt[3]{p^{11}}$

Rewrite $p^{11}$ as ${(p^{3})}^{3} p^{2}$ .

Factor out $p^{9}$ .

$p \sqrt{p} \sqrt[3]{p^{9} p^{2}}$

Rewrite $p^{9}$ as ${(p^{3})}^{3}$ .

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

Pull terms out from under the radical.

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

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

Move $p^{3}$ .

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

Multiply $p^{3}$ by $p$ .

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

$p^{3} p^{1} \sqrt{p} \sqrt[3]{p^{2}}$

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

$p^{3 + 1} \sqrt{p} \sqrt[3]{p^{2}}$

Add $3$ and $1$ .

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

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

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{p^{2}}$ as $p^{\frac{2}{3}}$ .

$p^{4} (p^{\frac{2}{3}} \sqrt{p})$

Rewrite $p^{\frac{2}{3}}$ as $p^{\frac{4}{6}}$ .

$p^{4} (p^{\frac{4}{6}} \sqrt{p})$

Rewrite $p^{\frac{4}{6}}$ as $\sqrt[6]{p^{4}}$ .

$p^{4} (\sqrt[6]{p^{4}} \sqrt{p})$

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

$p^{4} (\sqrt[6]{p^{4}} p^{\frac{1}{2}})$

Rewrite $p^{\frac{1}{2}}$ as $p^{\frac{3}{6}}$ .

$p^{4} (\sqrt[6]{p^{4}} p^{\frac{3}{6}})$

Rewrite $p^{\frac{3}{6}}$ as $\sqrt[6]{p^{3}}$ .

$p^{4} (\sqrt[6]{p^{4}} \sqrt[6]{p^{3}})$

Combine using the product rule for radicals.

$p^{4} \sqrt[6]{p^{4} p^{3}}$

Multiply $p^{4}$ by $p^{3}$ by adding the exponents.

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

$p^{4} \sqrt[6]{p^{4 + 3}}$

Add $4$ and $3$ .

$p^{4} \sqrt[6]{p^{7}}$

Factor out $p^{6}$ .

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

Pull terms out from under the radical.

$p^{4} (p \sqrt[6]{p})$

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

Move $p$ .

$p \cdot p^{4} \sqrt[6]{p}$

Multiply $p$ by $p^{4}$ .

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

$p^{1} p^{4} \sqrt[6]{p}$

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

$p^{1 + 4} \sqrt[6]{p}$

Add $1$ and $4$ .

$p^{5} \sqrt[6]{p}$

Simplify square root of p^3 cube root of p^11

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