Algebra Examples

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

Step 1

Move $y^{\frac{2}{7}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 2

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

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Step 2.1

Move $y^{- \frac{2}{7}}$ .

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

Step 2.2

Multiply $y^{- \frac{2}{7}}$ by $y$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Write $1$ as a fraction with a common denominator.

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $- 2$ and $7$ .

$\frac{x^{2}}{y^{\frac{5}{7}} \cdot x^{\frac{3}{4}}}$

Step 3

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

$\frac{x^{2} x^{- \frac{3}{4}}}{y^{\frac{5}{7}}}$

Step 4

Multiply $x^{2}$ by $x^{- \frac{3}{4}}$ 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.

$\frac{x^{2 - \frac{3}{4}}}{y^{\frac{5}{7}}}$

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x^{2 \cdot \frac{4}{4} - \frac{3}{4}}}{y^{\frac{5}{7}}}$

Step 4.3

Combine $2$ and $\frac{4}{4}$ .

$\frac{x^{\frac{2 \cdot 4}{4} - \frac{3}{4}}}{y^{\frac{5}{7}}}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{x^{\frac{2 \cdot 4 - 3}{4}}}{y^{\frac{5}{7}}}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $4$ .

$\frac{x^{\frac{8 - 3}{4}}}{y^{\frac{5}{7}}}$

Step 4.5.2

Subtract $3$ from $8$ .

$\frac{x^{\frac{5}{4}}}{y^{\frac{5}{7}}}$