Algebra Examples

$\frac{3 x^{- \frac{1}{2}} \cdot 3 x^{\frac{1}{2}} y^{- \frac{1}{3}}}{3 y^{- \frac{7}{4}}}$

Step 1

Multiply $x^{- \frac{1}{2}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 1.1

Move $x^{\frac{1}{2}}$ .

$\frac{3 (x^{\frac{1}{2}} x^{- \frac{1}{2}}) \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 1.2

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

$\frac{3 x^{\frac{1}{2} - \frac{1}{2}} \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{3 x^{\frac{1 - 1}{2}} \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 1.4

Subtract $1$ from $1$ .

$\frac{3 x^{\frac{0}{2}} \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 1.5

Divide $0$ by $2$ .

$\frac{3 x^{0} \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 2

Simplify $3 x^{0} \cdot (3 y^{- \frac{1}{3}})$ .

$\frac{3 \cdot (3 y^{- \frac{1}{3}})}{3 y^{- \frac{7}{4}}}$

Step 3

Move $y^{- \frac{7}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 \cdot (3 y^{- \frac{1}{3}}) y^{\frac{7}{4}}}{3}$

Step 4

Multiply $y^{- \frac{1}{3}}$ by $y^{\frac{7}{4}}$ by adding the exponents.

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Step 4.1

Move $y^{\frac{7}{4}}$ .

$\frac{3 \cdot (3 (y^{\frac{7}{4}} y^{- \frac{1}{3}}))}{3}$

Step 4.2

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

$\frac{3 \cdot (3 y^{\frac{7}{4} - \frac{1}{3}})}{3}$

Step 4.3

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 \cdot (3 y^{\frac{7}{4} \cdot \frac{3}{3} - \frac{1}{3}})}{3}$

Step 4.4

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 \cdot (3 y^{\frac{7}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}})}{3}$

Step 4.5

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

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Step 4.5.1

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{3 \cdot (3 y^{\frac{7 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}})}{3}$

Step 4.5.2

Multiply $4$ by $3$ .

$\frac{3 \cdot (3 y^{\frac{7 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}})}{3}$

Step 4.5.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{3 \cdot (3 y^{\frac{7 \cdot 3}{12} - \frac{4}{3 \cdot 4}})}{3}$

Step 4.5.4

Multiply $3$ by $4$ .

$\frac{3 \cdot (3 y^{\frac{7 \cdot 3}{12} - \frac{4}{12}})}{3}$

Step 4.6

Combine the numerators over the common denominator.

$\frac{3 \cdot (3 y^{\frac{7 \cdot 3 - 4}{12}})}{3}$

Step 4.7

Simplify the numerator.

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Step 4.7.1

Multiply $7$ by $3$ .

$\frac{3 \cdot (3 y^{\frac{21 - 4}{12}})}{3}$

Step 4.7.2

Subtract $4$ from $21$ .

$\frac{3 \cdot (3 y^{\frac{17}{12}})}{3}$

Step 5

Cancel the common factor.

$\frac{3 \cdot (3 y^{\frac{17}{12}})}{3}$

Step 6

Divide $3 y^{\frac{17}{12}}$ by $1$ .

$3 y^{\frac{17}{12}}$