Basic Math Examples

$\frac{{(r^{\frac{1}{3}} s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $r^{\frac{1}{3}} s^{\frac{2}{7}}$ .

$\frac{{(r^{\frac{1}{3}})}^{21} {(s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1.2

Multiply the exponents in ${(r^{\frac{1}{3}})}^{21}$ .

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Step 1.2.1

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

$\frac{r^{\frac{1}{3} \cdot 21} {(s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1.2.2

Cancel the common factor of $3$ .

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Step 1.2.2.1

Factor $3$ out of $21$ .

$\frac{r^{\frac{1}{3} \cdot (3 (7))} {(s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1.2.2.2

Cancel the common factor.

$\frac{r^{\frac{1}{3} \cdot (3 \cdot 7)} {(s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{r^{7} {(s^{\frac{2}{7}})}^{21}}{r^{2}}$

Step 1.3

Multiply the exponents in ${(s^{\frac{2}{7}})}^{21}$ .

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Step 1.3.1

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

$\frac{r^{7} s^{\frac{2}{7} \cdot 21}}{r^{2}}$

Step 1.3.2

Cancel the common factor of $7$ .

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Step 1.3.2.1

Factor $7$ out of $21$ .

$\frac{r^{7} s^{\frac{2}{7} \cdot (7 (3))}}{r^{2}}$

Step 1.3.2.2

Cancel the common factor.

$\frac{r^{7} s^{\frac{2}{7} \cdot (7 \cdot 3)}}{r^{2}}$

Step 1.3.2.3

Rewrite the expression.

$\frac{r^{7} s^{2 \cdot 3}}{r^{2}}$

Step 1.3.3

Multiply $2$ by $3$ .

$\frac{r^{7} s^{6}}{r^{2}}$

Step 2

Cancel the common factor of $r^{7}$ and $r^{2}$ .

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Step 2.1

Factor $r^{2}$ out of $r^{7} s^{6}$ .

$\frac{r^{2} (r^{5} s^{6})}{r^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{r^{2} (r^{5} s^{6})}{r^{2} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{r^{2} (r^{5} s^{6})}{r^{2} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{r^{5} s^{6}}{1}$

Step 2.2.4

Divide $r^{5} s^{6}$ by $1$ .

$r^{5} s^{6}$