Algebra Examples

$\frac{x^{\frac{3}{2}} y^{\frac{7}{3}}}{x^{3} y^{\frac{2}{9}}}$

Step 1

Move $x^{\frac{3}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{y^{\frac{7}{3}}}{x^{3} y^{\frac{2}{9}} x^{- \frac{3}{2}}}$

Step 2

Multiply $x^{3}$ by $x^{- \frac{3}{2}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{3}{2}}$ .

$\frac{y^{\frac{7}{3}}}{x^{- \frac{3}{2}} x^{3} y^{\frac{2}{9}}}$

Step 2.2

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

$\frac{y^{\frac{7}{3}}}{x^{- \frac{3}{2} + 3} y^{\frac{2}{9}}}$

Step 2.3

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y^{\frac{7}{3}}}{x^{- \frac{3}{2} + 3 \cdot \frac{2}{2}} y^{\frac{2}{9}}}$

Step 2.4

Combine $3$ and $\frac{2}{2}$ .

$\frac{y^{\frac{7}{3}}}{x^{- \frac{3}{2} + \frac{3 \cdot 2}{2}} y^{\frac{2}{9}}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{y^{\frac{7}{3}}}{x^{\frac{- 3 + 3 \cdot 2}{2}} y^{\frac{2}{9}}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $2$ .

$\frac{y^{\frac{7}{3}}}{x^{\frac{- 3 + 6}{2}} y^{\frac{2}{9}}}$

Step 2.6.2

Add $- 3$ and $6$ .

$\frac{y^{\frac{7}{3}}}{x^{\frac{3}{2}} y^{\frac{2}{9}}}$

Step 3

Move $y^{\frac{2}{9}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{y^{\frac{7}{3}} y^{- \frac{2}{9}}}{x^{\frac{3}{2}}}$

Step 4

Multiply $y^{\frac{7}{3}}$ by $y^{- \frac{2}{9}}$ by adding the exponents.

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Step 4.1

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

$\frac{y^{\frac{7}{3} - \frac{2}{9}}}{x^{\frac{3}{2}}}$

Step 4.2

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

$\frac{y^{\frac{7}{3} \cdot \frac{3}{3} - \frac{2}{9}}}{x^{\frac{3}{2}}}$

Step 4.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

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

$\frac{y^{\frac{7 \cdot 3}{3 \cdot 3} - \frac{2}{9}}}{x^{\frac{3}{2}}}$

Step 4.3.2

Multiply $3$ by $3$ .

$\frac{y^{\frac{7 \cdot 3}{9} - \frac{2}{9}}}{x^{\frac{3}{2}}}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{y^{\frac{7 \cdot 3 - 2}{9}}}{x^{\frac{3}{2}}}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $7$ by $3$ .

$\frac{y^{\frac{21 - 2}{9}}}{x^{\frac{3}{2}}}$

Step 4.5.2

Subtract $2$ from $21$ .

$\frac{y^{\frac{19}{9}}}{x^{\frac{3}{2}}}$