Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $x^{\frac{2}{3}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 3.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.4

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

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

Step 3.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.5.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 3.5.2

Multiply $2$ by $3$ .

$x^{- \frac{3}{6} + \frac{2}{3} \cdot \frac{2}{2}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 3.5.3

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$x^{- \frac{3}{6} + \frac{2 \cdot 2}{3 \cdot 2}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 3.5.4

Multiply $3$ by $2$ .

$x^{- \frac{3}{6} + \frac{2 \cdot 2}{6}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 3.6

Combine the numerators over the common denominator.

$x^{\frac{- 3 + 2 \cdot 2}{6}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 3.7

Simplify the numerator.

Tap for more steps...

Step 3.7.1

Multiply $2$ by $2$ .

$x^{\frac{- 3 + 4}{6}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 3.7.2

Add $- 3$ and $4$ .

$x^{\frac{1}{6}} y^{- \frac{1}{4}} y^{\frac{1}{2}}$

Step 4

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

Tap for more steps...

Step 4.1

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

$x^{\frac{1}{6}} (y^{\frac{1}{2}} y^{- \frac{1}{4}})$

Step 4.2

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

$x^{\frac{1}{6}} y^{\frac{1}{2} - \frac{1}{4}}$

Step 4.3

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

$x^{\frac{1}{6}} y^{\frac{1}{2} \cdot \frac{2}{2} - \frac{1}{4}}$

Step 4.4

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

Tap for more steps...

Step 4.4.1

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

$x^{\frac{1}{6}} y^{\frac{2}{2 \cdot 2} - \frac{1}{4}}$

Step 4.4.2

Multiply $2$ by $2$ .

$x^{\frac{1}{6}} y^{\frac{2}{4} - \frac{1}{4}}$

Step 4.5

Combine the numerators over the common denominator.

$x^{\frac{1}{6}} y^{\frac{2 - 1}{4}}$

Step 4.6

Subtract $1$ from $2$ .

$x^{\frac{1}{6}} y^{\frac{1}{4}}$