Simplify fifth root of u^11 fourth root of u^11

$\sqrt[5]{u^{11}} \sqrt[4]{u^{11}}$

Rewrite $u^{11}$ as ${(u^{2})}^{5} u$ .

Factor out $u^{10}$ .

$\sqrt[5]{u^{10} u} \sqrt[4]{u^{11}}$

Rewrite $u^{10}$ as ${(u^{2})}^{5}$ .

$\sqrt[5]{{(u^{2})}^{5} u} \sqrt[4]{u^{11}}$

Pull terms out from under the radical.

$u^{2} \sqrt[5]{u} \sqrt[4]{u^{11}}$

Rewrite $u^{11}$ as ${(u^{2})}^{4} u^{3}$ .

Factor out $u^{8}$ .

$u^{2} \sqrt[5]{u} \sqrt[4]{u^{8} u^{3}}$

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

$u^{2} \sqrt[5]{u} \sqrt[4]{{(u^{2})}^{4} u^{3}}$

Pull terms out from under the radical.

$u^{2} \sqrt[5]{u} (u^{2} \sqrt[4]{u^{3}})$

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

Move $u^{2}$ .

$u^{2} u^{2} \sqrt[5]{u} \sqrt[4]{u^{3}}$

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

$u^{2 + 2} \sqrt[5]{u} \sqrt[4]{u^{3}}$

Add $2$ and $2$ .

$u^{4} \sqrt[5]{u} \sqrt[4]{u^{3}}$

Multiply $u^{4} \sqrt[5]{u} \sqrt[4]{u^{3}}$ .

Rewrite the expression using the least common index of $20$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{u^{3}}$ as $u^{\frac{3}{4}}$ .

$u^{4} (u^{\frac{3}{4}} \sqrt[5]{u})$

Rewrite $u^{\frac{3}{4}}$ as $u^{\frac{15}{20}}$ .

$u^{4} (u^{\frac{15}{20}} \sqrt[5]{u})$

Rewrite $u^{\frac{15}{20}}$ as $\sqrt[20]{u^{15}}$ .

$u^{4} (\sqrt[20]{u^{15}} \sqrt[5]{u})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{u}$ as $u^{\frac{1}{5}}$ .

$u^{4} (\sqrt[20]{u^{15}} u^{\frac{1}{5}})$

Rewrite $u^{\frac{1}{5}}$ as $u^{\frac{4}{20}}$ .

$u^{4} (\sqrt[20]{u^{15}} u^{\frac{4}{20}})$

Rewrite $u^{\frac{4}{20}}$ as $\sqrt[20]{u^{4}}$ .

$u^{4} (\sqrt[20]{u^{15}} \sqrt[20]{u^{4}})$

Combine using the product rule for radicals.

$u^{4} \sqrt[20]{u^{15} u^{4}}$

Multiply $u^{15}$ by $u^{4}$ by adding the exponents.

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

$u^{4} \sqrt[20]{u^{15 + 4}}$

Add $15$ and $4$ .

$u^{4} \sqrt[20]{u^{19}}$