Basic Math Examples

$\frac{{(r^{\frac{1}{4}} y^{\frac{3}{9}})}^{36}}{r^{3}}$

Step 1

Cancel the common factor of $3$ and $9$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{{(r^{\frac{1}{4}} y^{\frac{3 (1)}{9}})}^{36}}{r^{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{{(r^{\frac{1}{4}} y^{\frac{3 \cdot 1}{3 \cdot 3}})}^{36}}{r^{3}}$

Step 1.2.2

Cancel the common factor.

$\frac{{(r^{\frac{1}{4}} y^{\frac{3 \cdot 1}{3 \cdot 3}})}^{36}}{r^{3}}$

Step 1.2.3

Rewrite the expression.

$\frac{{(r^{\frac{1}{4}} y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $r^{\frac{1}{4}} y^{\frac{1}{3}}$ .

$\frac{{(r^{\frac{1}{4}})}^{36} {(y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2.2

Multiply the exponents in ${(r^{\frac{1}{4}})}^{36}$ .

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Step 2.2.1

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

$\frac{r^{\frac{1}{4} \cdot 36} {(y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2.2.2

Cancel the common factor of $4$ .

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Step 2.2.2.1

Factor $4$ out of $36$ .

$\frac{r^{\frac{1}{4} \cdot (4 (9))} {(y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2.2.2.2

Cancel the common factor.

$\frac{r^{\frac{1}{4} \cdot (4 \cdot 9)} {(y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{r^{9} {(y^{\frac{1}{3}})}^{36}}{r^{3}}$

Step 2.3

Multiply the exponents in ${(y^{\frac{1}{3}})}^{36}$ .

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Step 2.3.1

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

$\frac{r^{9} y^{\frac{1}{3} \cdot 36}}{r^{3}}$

Step 2.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1

Factor $3$ out of $36$ .

$\frac{r^{9} y^{\frac{1}{3} \cdot (3 (12))}}{r^{3}}$

Step 2.3.2.2

Cancel the common factor.

$\frac{r^{9} y^{\frac{1}{3} \cdot (3 \cdot 12)}}{r^{3}}$

Step 2.3.2.3

Rewrite the expression.

$\frac{r^{9} y^{12}}{r^{3}}$

Step 3

Cancel the common factor of $r^{9}$ and $r^{3}$ .

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Step 3.1

Factor $r^{3}$ out of $r^{9} y^{12}$ .

$\frac{r^{3} (r^{6} y^{12})}{r^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{r^{3} (r^{6} y^{12})}{r^{3} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{r^{3} (r^{6} y^{12})}{r^{3} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{r^{6} y^{12}}{1}$

Step 3.2.4

Divide $r^{6} y^{12}$ by $1$ .

$r^{6} y^{12}$