# How do you simplify (x^3y^4)/( x^9y^2) using only positive exponents?

Jun 30, 2016

${y}^{2} / {x}^{6}$

#### Explanation:

If we expand $\frac{{x}^{3} {y}^{4}}{{x}^{9} {y}^{2}}$

We see that the number of variables in the fraction become

$\frac{x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y}{x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y}$

We can now cancel the similar variables

$\frac{\cancel{x \cdot x \cdot x} \cdot \cancel{y \cdot y} \cdot y \cdot y}{\cancel{x \cdot x \cdot x} \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot \cancel{y \cdot y}}$

We are left with

$\frac{y \cdot y}{x \cdot x \cdot x \cdot x \cdot x \cdot x}$

Which becomes

${y}^{2} / {x}^{6}$

Or by using the properties of exponents

We can change $\frac{{x}^{3} {y}^{4}}{{x}^{9} {y}^{2}}$ to

${x}^{3} {x}^{-} 9 {y}^{4} {y}^{-} 2$

Which becomes

${x}^{3 - 9} {y}^{4 - 2}$

Which becomes
${x}^{-} 6 y 2$

Eliminating the negative exponent by placing it in the denominator we get

${y}^{2} / {x}^{6}$