Algebra Examples

$\frac{3 y^{- \frac{5}{4}}}{y^{- 1} \cdot 2 y^{- \frac{1}{3}}}$

Step 1

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

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Step 1.1

Move $y^{- \frac{1}{3}}$ .

$\frac{3 y^{- \frac{5}{4}}}{y^{- \frac{1}{3}} y^{- 1} \cdot 2}$

Step 1.2

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

$\frac{3 y^{- \frac{5}{4}}}{y^{- \frac{1}{3} - 1} \cdot 2}$

Step 1.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 y^{- \frac{5}{4}}}{y^{- \frac{1}{3} - 1 \cdot \frac{3}{3}} \cdot 2}$

Step 1.4

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

$\frac{3 y^{- \frac{5}{4}}}{y^{- \frac{1}{3} + \frac{- 1 \cdot 3}{3}} \cdot 2}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 y^{- \frac{5}{4}}}{y^{\frac{- 1 - 1 \cdot 3}{3}} \cdot 2}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 1$ by $3$ .

$\frac{3 y^{- \frac{5}{4}}}{y^{\frac{- 1 - 3}{3}} \cdot 2}$

Step 1.6.2

Subtract $3$ from $- 1$ .

$\frac{3 y^{- \frac{5}{4}}}{y^{\frac{- 4}{3}} \cdot 2}$

Step 1.7

Move the negative in front of the fraction.

$\frac{3 y^{- \frac{5}{4}}}{y^{- \frac{4}{3}} \cdot 2}$

Step 2

Move $y^{- \frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 y^{- \frac{5}{4}} y^{\frac{4}{3}}}{2}$

Step 3

Multiply $y^{- \frac{5}{4}}$ by $y^{\frac{4}{3}}$ by adding the exponents.

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Step 3.1

Move $y^{\frac{4}{3}}$ .

$\frac{3 (y^{\frac{4}{3}} y^{- \frac{5}{4}})}{2}$

Step 3.2

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

$\frac{3 y^{\frac{4}{3} - \frac{5}{4}}}{2}$

Step 3.3

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

$\frac{3 y^{\frac{4}{3} \cdot \frac{4}{4} - \frac{5}{4}}}{2}$

Step 3.4

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 y^{\frac{4}{3} \cdot \frac{4}{4} - \frac{5}{4} \cdot \frac{3}{3}}}{2}$

Step 3.5

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

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Step 3.5.1

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

$\frac{3 y^{\frac{4 \cdot 4}{3 \cdot 4} - \frac{5}{4} \cdot \frac{3}{3}}}{2}$

Step 3.5.2

Multiply $3$ by $4$ .

$\frac{3 y^{\frac{4 \cdot 4}{12} - \frac{5}{4} \cdot \frac{3}{3}}}{2}$

Step 3.5.3

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{3 y^{\frac{4 \cdot 4}{12} - \frac{5 \cdot 3}{4 \cdot 3}}}{2}$

Step 3.5.4

Multiply $4$ by $3$ .

$\frac{3 y^{\frac{4 \cdot 4}{12} - \frac{5 \cdot 3}{12}}}{2}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{3 y^{\frac{4 \cdot 4 - 5 \cdot 3}{12}}}{2}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply $4$ by $4$ .

$\frac{3 y^{\frac{16 - 5 \cdot 3}{12}}}{2}$

Step 3.7.2

Multiply $- 5$ by $3$ .

$\frac{3 y^{\frac{16 - 15}{12}}}{2}$

Step 3.7.3

Subtract $15$ from $16$ .

$\frac{3 y^{\frac{1}{12}}}{2}$