Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $x^{\frac{7}{4}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

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

Step 3.4.2

Multiply $2$ by $2$ .

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Add $- 2$ and $7$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Combine the numerators over the common denominator.

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

Step 4.4

Add $2$ and $3$ .

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

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