Simplify the Radical Expression 21 root of c^-3*c^-4

$\sqrt[21]{c^{- 3} \cdot c^{- 4}}$

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

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

$\sqrt[21]{c^{- 3 - 4}}$

Subtract $4$ from $- 3$ .

$\sqrt[21]{c^{- 7}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt[21]{\frac{1}{c^{7}}}$

Rewrite $1$ as $1^{7}$ .

$\sqrt[21]{\frac{1^{7}}{c^{7}}}$

Rewrite $\frac{1^{7}}{c^{7}}$ as ${(\frac{1}{c})}^{7}$ .

$\sqrt[21]{{(\frac{1}{c})}^{7}}$

Rewrite $\sqrt[21]{{(\frac{1}{c})}^{7}}$ as $\sqrt[3]{\sqrt[7]{{(\frac{1}{c})}^{7}}}$ .

$\sqrt[3]{\sqrt[7]{{(\frac{1}{c})}^{7}}}$

Pull terms out from under the radical.

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

Rewrite $\sqrt[3]{\frac{1}{c}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{c}}$ .

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

Any root of $1$ is $1$ .

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

Multiply $\frac{1}{\sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

$\frac{1}{\sqrt[3]{c}} \cdot \frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

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

Raise $\sqrt[3]{c}$ to the power of $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite ${\sqrt[3]{c}}^{3}$ as $c$ .

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

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

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

$\frac{{\sqrt[3]{c}}^{2}}{c^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Rewrite ${\sqrt[3]{c}}^{2}$ as ${(c^{2})}^{\frac{1}{3}}$ .

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

Simplify the Radical Expression 21 root of c^-3*c^-4

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