Simplify (-20xy^(-1/2))/(4x^3y^(-3/4))

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $2$ from $3$ .

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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