Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Add $- 1$ and $2$ .

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

Step 3.2

Multiply $y^{\frac{3}{4}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

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

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

Step 3.2.4

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

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Step 3.2.4.1

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

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

Step 3.2.4.2

Multiply $2$ by $2$ .

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

Step 3.2.5

Combine the numerators over the common denominator.

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

Step 3.2.6

Add $- 2$ and $3$ .

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

Step 4

Factor $3$ out of $6 x^{\frac{1}{2}} y^{\frac{1}{4}}$ .

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

Step 5

Cancel the common factors.

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Step 5.1

Factor $3$ out of $3$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 5.4

Divide $2 x^{\frac{1}{2}} y^{\frac{1}{4}}$ by $1$ .

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