Simplify fifth root of h^6 cube root of h

$\sqrt[5]{h^{6}} \sqrt[3]{h}$

Factor out $h^{5}$ .

$\sqrt[5]{h^{5} h} \sqrt[3]{h}$

Pull terms out from under the radical.

$h \sqrt[5]{h} \sqrt[3]{h}$

Multiply $h \sqrt[5]{h} \sqrt[3]{h}$ .

Rewrite the expression using the least common index of $15$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{h}$ as $h^{\frac{1}{3}}$ .

$h (h^{\frac{1}{3}} \sqrt[5]{h})$

Rewrite $h^{\frac{1}{3}}$ as $h^{\frac{5}{15}}$ .

$h (h^{\frac{5}{15}} \sqrt[5]{h})$

Rewrite $h^{\frac{5}{15}}$ as $\sqrt[15]{h^{5}}$ .

$h (\sqrt[15]{h^{5}} \sqrt[5]{h})$

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

$h (\sqrt[15]{h^{5}} h^{\frac{1}{5}})$

Rewrite $h^{\frac{1}{5}}$ as $h^{\frac{3}{15}}$ .

$h (\sqrt[15]{h^{5}} h^{\frac{3}{15}})$

Rewrite $h^{\frac{3}{15}}$ as $\sqrt[15]{h^{3}}$ .

$h (\sqrt[15]{h^{5}} \sqrt[15]{h^{3}})$

Combine using the product rule for radicals.

$h \sqrt[15]{h^{5} h^{3}}$

Multiply $h^{5}$ by $h^{3}$ by adding the exponents.

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

$h \sqrt[15]{h^{5 + 3}}$

Add $5$ and $3$ .

$h \sqrt[15]{h^{8}}$