Simplify the Radical Expression ( fifth root of h^11)/( sixth root of h^5)

$\frac{\sqrt[5]{h^{11}}}{\sqrt[6]{h^{5}}}$

Simplify the numerator.

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

Factor out $h^{10}$ .

$\frac{\sqrt[5]{h^{10} h}}{\sqrt[6]{h^{5}}}$

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

$\frac{\sqrt[5]{{(h^{2})}^{5} h}}{\sqrt[6]{h^{5}}}$

Pull terms out from under the radical.

$\frac{h^{2} \sqrt[5]{h}}{\sqrt[6]{h^{5}}}$

Multiply $\frac{h^{2} \sqrt[5]{h}}{\sqrt[6]{h^{5}}}$ by $\frac{{\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{5}}$ .

$\frac{h^{2} \sqrt[5]{h}}{\sqrt[6]{h^{5}}} \cdot \frac{{\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{5}}$

Combine and simplify the denominator.

Multiply $\frac{h^{2} \sqrt[5]{h}}{\sqrt[6]{h^{5}}}$ by $\frac{{\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{5}}$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{\sqrt[6]{h^{5}} {\sqrt[6]{h^{5}}}^{5}}$

Raise $\sqrt[6]{h^{5}}$ to the power of $1$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{1} {\sqrt[6]{h^{5}}}^{5}}$

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

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{1 + 5}}$

Add $1$ and $5$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{{\sqrt[6]{h^{5}}}^{6}}$

Rewrite ${\sqrt[6]{h^{5}}}^{6}$ as $h^{5}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{h^{5}}$ as $h^{\frac{5}{6}}$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{{(h^{\frac{5}{6}})}^{6}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{5}{6} \cdot 6}}$

Combine $\frac{5}{6}$ and $6$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{5 \cdot 6}{6}}}$

Multiply $5$ by $6$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{30}{6}}}$

Cancel the common factor of $30$ and $6$ .

Factor $6$ out of $30$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{6 \cdot 5}{6}}}$

Cancel the common factors.

Factor $6$ out of $6$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{6 \cdot 5}{6 (1)}}}$

Cancel the common factor.

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{6 \cdot 5}{6 \cdot 1}}}$

Rewrite the expression.

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{\frac{5}{1}}}$

Divide $5$ by $1$ .

$\frac{h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}}{h^{5}}$

Cancel the common factor of $h^{2}$ and $h^{5}$ .

Factor $h^{2}$ out of $h^{2} \sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5}$ .

$\frac{h^{2} (\sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5})}{h^{5}}$

Cancel the common factors.

Factor $h^{2}$ out of $h^{5}$ .

$\frac{h^{2} (\sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5})}{h^{2} h^{3}}$

Cancel the common factor.

$\frac{h^{2} (\sqrt[5]{h} {\sqrt[6]{h^{5}}}^{5})}{h^{2} h^{3}}$

Rewrite the expression.

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

Simplify the numerator.

Rewrite ${\sqrt[6]{h^{5}}}^{5}$ as ${({(h^{5})}^{5})}^{\frac{1}{6}}$ .

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

Multiply the exponents in ${(h^{5})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $5$ by $5$ .

$\frac{\sqrt[5]{h} \sqrt[6]{h^{25}}}{h^{3}}$

Rewrite $h^{25}$ as ${(h^{4})}^{6} h$ .

Factor out $h^{24}$ .

$\frac{\sqrt[5]{h} \sqrt[6]{h^{24} h}}{h^{3}}$

Rewrite $h^{24}$ as ${(h^{4})}^{6}$ .

$\frac{\sqrt[5]{h} \sqrt[6]{{(h^{4})}^{6} h}}{h^{3}}$

Pull terms out from under the radical.

$\frac{\sqrt[5]{h} (| h^{4} | \sqrt[6]{h})}{h^{3}}$

Remove non-negative terms from the absolute value.

$\frac{\sqrt[5]{h} h^{4} \sqrt[6]{h}}{h^{3}}$

Combine exponents.

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

$\frac{h^{\frac{1}{5}} h^{4} \sqrt[6]{h}}{h^{3}}$

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

$\frac{h^{\frac{1}{5} + 4} \sqrt[6]{h}}{h^{3}}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{h^{\frac{1}{5} + 4 \cdot \frac{5}{5}} \sqrt[6]{h}}{h^{3}}$

Combine $4$ and $\frac{5}{5}$ .

$\frac{h^{\frac{1}{5} + \frac{4 \cdot 5}{5}} \sqrt[6]{h}}{h^{3}}$

Combine the numerators over the common denominator.

$\frac{h^{\frac{1 + 4 \cdot 5}{5}} \sqrt[6]{h}}{h^{3}}$

Simplify the numerator.

Multiply $4$ by $5$ .

$\frac{h^{\frac{1 + 20}{5}} \sqrt[6]{h}}{h^{3}}$

Add $1$ and $20$ .

$\frac{h^{\frac{21}{5}} \sqrt[6]{h}}{h^{3}}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{h}$ as $h^{\frac{1}{6}}$ .

$\frac{h^{\frac{21}{5}} h^{\frac{1}{6}}}{h^{3}}$

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

$\frac{h^{\frac{21}{5} + \frac{1}{6}}}{h^{3}}$

To write $\frac{21}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{h^{\frac{21}{5} \cdot \frac{6}{6} + \frac{1}{6}}}{h^{3}}$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{h^{\frac{21}{5} \cdot \frac{6}{6} + \frac{1}{6} \cdot \frac{5}{5}}}{h^{3}}$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{21}{5}$ by $\frac{6}{6}$ .

$\frac{h^{\frac{21 \cdot 6}{5 \cdot 6} + \frac{1}{6} \cdot \frac{5}{5}}}{h^{3}}$

Multiply $5$ by $6$ .

$\frac{h^{\frac{21 \cdot 6}{30} + \frac{1}{6} \cdot \frac{5}{5}}}{h^{3}}$

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{h^{\frac{21 \cdot 6}{30} + \frac{5}{6 \cdot 5}}}{h^{3}}$

Multiply $6$ by $5$ .

$\frac{h^{\frac{21 \cdot 6}{30} + \frac{5}{30}}}{h^{3}}$

Combine the numerators over the common denominator.

$\frac{h^{\frac{21 \cdot 6 + 5}{30}}}{h^{3}}$

Simplify the numerator.

Multiply $21$ by $6$ .

$\frac{h^{\frac{126 + 5}{30}}}{h^{3}}$

Add $126$ and $5$ .

$\frac{h^{\frac{131}{30}}}{h^{3}}$

Move $h^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$h^{\frac{131}{30}} h^{- 3}$

Multiply $h^{\frac{131}{30}}$ by $h^{- 3}$ by adding the exponents.

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

$h^{\frac{131}{30} - 3}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$h^{\frac{131}{30} - 3 \cdot \frac{30}{30}}$

Combine $- 3$ and $\frac{30}{30}$ .

$h^{\frac{131}{30} + \frac{- 3 \cdot 30}{30}}$

Combine the numerators over the common denominator.

$h^{\frac{131 - 3 \cdot 30}{30}}$

Simplify the numerator.

Multiply $- 3$ by $30$ .

$h^{\frac{131 - 90}{30}}$

Subtract $90$ from $131$ .

$h^{\frac{41}{30}}$

Simplify the Radical Expression ( fifth root of h^11)/( sixth root of h^5)

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