Algebra Examples

$\frac{{(3 y^{\frac{1}{4}})}^{3}}{y^{\frac{1}{12}}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{3^{3} {(y^{\frac{1}{4}})}^{3}}{y^{\frac{1}{12}}}$

Step 1.2

Raise $3$ to the power of $3$ .

$\frac{27 {(y^{\frac{1}{4}})}^{3}}{y^{\frac{1}{12}}}$

Step 1.3

Multiply the exponents in ${(y^{\frac{1}{4}})}^{3}$ .

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Step 1.3.1

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

$\frac{27 y^{\frac{1}{4} \cdot 3}}{y^{\frac{1}{12}}}$

Step 1.3.2

Combine $\frac{1}{4}$ and $3$ .

$\frac{27 y^{\frac{3}{4}}}{y^{\frac{1}{12}}}$

Step 2

Move $y^{\frac{1}{12}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$27 y^{\frac{3}{4}} y^{- \frac{1}{12}}$

Step 3

Multiply $y^{\frac{3}{4}}$ by $y^{- \frac{1}{12}}$ by adding the exponents.

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Step 3.1

Move $y^{- \frac{1}{12}}$ .

$27 (y^{- \frac{1}{12}} y^{\frac{3}{4}})$

Step 3.2

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

$27 y^{- \frac{1}{12} + \frac{3}{4}}$

Step 3.3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$27 y^{- \frac{1}{12} + \frac{3}{4} \cdot \frac{3}{3}}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$27 y^{- \frac{1}{12} + \frac{3 \cdot 3}{4 \cdot 3}}$

Step 3.4.2

Multiply $4$ by $3$ .

$27 y^{- \frac{1}{12} + \frac{3 \cdot 3}{12}}$

Step 3.5

Combine the numerators over the common denominator.

$27 y^{\frac{- 1 + 3 \cdot 3}{12}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $3$ by $3$ .

$27 y^{\frac{- 1 + 9}{12}}$

Step 3.6.2

Add $- 1$ and $9$ .

$27 y^{\frac{8}{12}}$

Step 3.7

Cancel the common factor of $8$ and $12$ .

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Step 3.7.1

Factor $4$ out of $8$ .

$27 y^{\frac{4 (2)}{12}}$

Step 3.7.2

Cancel the common factors.

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Step 3.7.2.1

Factor $4$ out of $12$ .

$27 y^{\frac{4 \cdot 2}{4 \cdot 3}}$

Step 3.7.2.2

Cancel the common factor.

$27 y^{\frac{4 \cdot 2}{4 \cdot 3}}$

Step 3.7.2.3

Rewrite the expression.

$27 y^{\frac{2}{3}}$