Basic Math Examples

\frac{\sqrt[3]{r^{19}}}{\sqrt[3]{27 s^{12}}}

$\frac{\sqrt[3]{r^{19}}}{\sqrt[3]{27 s^{12}}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

r^{19}

$r^{19}$ as

{(r^{6})}^{3} r

${(r^{6})}^{3} r$ .

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Step 1.1.1

Factor out

r^{18}

$r^{18}$ .

\frac{\sqrt[3]{r^{18} r}}{\sqrt[3]{27 s^{12}}}

$\frac{\sqrt[3]{r^{18} r}}{\sqrt[3]{27 s^{12}}}$

Step 1.1.2

Rewrite

r^{18}

$r^{18}$ as

{(r^{6})}^{3}

${(r^{6})}^{3}$ .

\frac{\sqrt[3]{{(r^{6})}^{3} r}}{\sqrt[3]{27 s^{12}}}

$\frac{\sqrt[3]{{(r^{6})}^{3} r}}{\sqrt[3]{27 s^{12}}}$

\frac{\sqrt[3]{{(r^{6})}^{3} r}}{\sqrt[3]{27 s^{12}}}

$\frac{\sqrt[3]{{(r^{6})}^{3} r}}{\sqrt[3]{27 s^{12}}}$

Step 1.2

Pull terms out from under the radical.

\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{27 s^{12}}}

$\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{27 s^{12}}}$

\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{27 s^{12}}}

$\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{27 s^{12}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

27 s^{12}

$27 s^{12}$ as

{(3 s^{4})}^{3}

${(3 s^{4})}^{3}$ .

\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{{(3 s^{4})}^{3}}}

$\frac{r^{6} \sqrt[3]{r}}{\sqrt[3]{{(3 s^{4})}^{3}}}$

Step 2.2

Pull terms out from under the radical, assuming real numbers.

\frac{r^{6} \sqrt[3]{r}}{3 s^{4}}

$\frac{r^{6} \sqrt[3]{r}}{3 s^{4}}$

\frac{r^{6} \sqrt[3]{r}}{3 s^{4}}

$\frac{r^{6} \sqrt[3]{r}}{3 s^{4}}$