Simplify ( square root of c^9)/( fourth root of c)

$\frac{\sqrt{c^{9}}}{\sqrt[4]{c}}$

Simplify the numerator.

Rewrite $c^{9}$ as ${(c^{4})}^{2} c$ .

Factor out $c^{8}$ .

$\frac{\sqrt{c^{8} c}}{\sqrt[4]{c}}$

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

$\frac{\sqrt{{(c^{4})}^{2} c}}{\sqrt[4]{c}}$

Pull terms out from under the radical.

$\frac{c^{4} \sqrt{c}}{\sqrt[4]{c}}$

Multiply $\frac{c^{4} \sqrt{c}}{\sqrt[4]{c}}$ by $\frac{{\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{3}}$ .

$\frac{c^{4} \sqrt{c}}{\sqrt[4]{c}} \cdot \frac{{\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{3}}$

Combine and simplify the denominator.

Multiply $\frac{c^{4} \sqrt{c}}{\sqrt[4]{c}}$ by $\frac{{\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{3}}$ .

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{\sqrt[4]{c} {\sqrt[4]{c}}^{3}}$

Raise $\sqrt[4]{c}$ to the power of $1$ .

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{1} {\sqrt[4]{c}}^{3}}$

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

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{1 + 3}}$

Add $1$ and $3$ .

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{{\sqrt[4]{c}}^{4}}$

Rewrite ${\sqrt[4]{c}}^{4}$ as $c$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{c}$ as $c^{\frac{1}{4}}$ .

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{{(c^{\frac{1}{4}})}^{4}}$

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

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{c^{\frac{1}{4} \cdot 4}}$

Combine $\frac{1}{4}$ and $4$ .

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{c^{\frac{4}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{c^{\frac{4}{4}}}$

Rewrite the expression.

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{c^{1}}$

Simplify.

$\frac{c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}}{c}$

Cancel the common factor of $c^{4}$ and $c$ .

Factor $c$ out of $c^{4} \sqrt{c} {\sqrt[4]{c}}^{3}$ .

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

Cancel the common factors.

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

$\frac{c (c^{3} \sqrt{c} {\sqrt[4]{c}}^{3})}{c^{1}}$

Factor $c$ out of $c^{1}$ .

$\frac{c (c^{3} \sqrt{c} {\sqrt[4]{c}}^{3})}{c \cdot 1}$

Cancel the common factor.

$\frac{c (c^{3} \sqrt{c} {\sqrt[4]{c}}^{3})}{c \cdot 1}$

Rewrite the expression.

$\frac{c^{3} \sqrt{c} {\sqrt[4]{c}}^{3}}{1}$

Divide $c^{3} \sqrt{c} {\sqrt[4]{c}}^{3}$ by $1$ .

$c^{3} \sqrt{c} {\sqrt[4]{c}}^{3}$

Rewrite ${\sqrt[4]{c}}^{3}$ as ${(c^{3})}^{\frac{1}{4}}$ .

$c^{3} \sqrt{c} \sqrt[4]{c^{3}}$

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

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

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

$c^{3} (\sqrt[4]{c^{3}} c^{\frac{1}{2}})$

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

$c^{3} (\sqrt[4]{c^{3}} c^{\frac{2}{4}})$

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

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

Combine using the product rule for radicals.

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

Multiply $c^{3}$ by $c^{2}$ by adding the exponents.

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

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

Add $3$ and $2$ .

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

Factor out $c^{4}$ .

$c^{3} \sqrt[4]{c^{4} c}$

Pull terms out from under the radical.

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

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

Move $c$ .

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

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

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

$c^{1} c^{3} \sqrt[4]{c}$

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

$c^{1 + 3} \sqrt[4]{c}$

Add $1$ and $3$ .

$c^{4} \sqrt[4]{c}$

Simplify ( square root of c^9)/( fourth root of c)

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