Algebra Examples

$\frac{- 20 x y^{- \frac{1}{2}}}{4 x^{3} y^{- \frac{3}{4}}}$

Step 1

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

$\frac{- 20 x y^{- \frac{1}{2}} y^{\frac{3}{4}}}{4 x^{3}}$

Step 2

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

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Step 2.1

Move $y^{\frac{3}{4}}$ .

$\frac{- 20 x (y^{\frac{3}{4}} y^{- \frac{1}{2}})}{4 x^{3}}$

Step 2.2

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

$\frac{- 20 x y^{\frac{3}{4} - \frac{1}{2}}}{4 x^{3}}$

Step 2.3

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

$\frac{- 20 x y^{\frac{3}{4} - \frac{1}{2} \cdot \frac{2}{2}}}{4 x^{3}}$

Step 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 2.4.1

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

$\frac{- 20 x y^{\frac{3}{4} - \frac{2}{2 \cdot 2}}}{4 x^{3}}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{- 20 x y^{\frac{3}{4} - \frac{2}{4}}}{4 x^{3}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 20 x y^{\frac{3 - 2}{4}}}{4 x^{3}}$

Step 2.6

Subtract $2$ from $3$ .

$\frac{- 20 x y^{\frac{1}{4}}}{4 x^{3}}$

Step 3

Factor $4$ out of $- 20 x y^{\frac{1}{4}}$ .

$\frac{4 (- 5 x y^{\frac{1}{4}})}{4 x^{3}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $4$ out of $4 x^{3}$ .

$\frac{4 (- 5 x y^{\frac{1}{4}})}{4 (x^{3})}$

Step 4.2

Cancel the common factor.

$\frac{4 (- 5 x y^{\frac{1}{4}})}{4 x^{3}}$

Step 4.3

Rewrite the expression.

$\frac{- 5 x y^{\frac{1}{4}}}{x^{3}}$

Step 5

Factor $x$ out of $- 5 x y^{\frac{1}{4}}$ .

$\frac{x (- 5 y^{\frac{1}{4}})}{x^{3}}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $x$ out of $x^{3}$ .

$\frac{x (- 5 y^{\frac{1}{4}})}{x \cdot x^{2}}$

Step 6.2

Cancel the common factor.

$\frac{x (- 5 y^{\frac{1}{4}})}{x \cdot x^{2}}$

Step 6.3

Rewrite the expression.

$\frac{- 5 y^{\frac{1}{4}}}{x^{2}}$

Step 7

Move the negative in front of the fraction.

$- \frac{5 y^{\frac{1}{4}}}{x^{2}}$