# How do you simplify and write x^4 / x^9 with positive exponents?

Jul 9, 2016

$\frac{1}{x} ^ 5$

#### Explanation:

To simplify this, we can take out common factors in the top and bottom:

x^4/x^9 = (x*x*x*x)/(x*x*x*x*x*x*x*x*x) = (cancelx*cancelx*cancelx*cancelx)/(cancelx*cancelx*cancelx*cancelx*x*x*x*x*x)

And we can get $\frac{1}{x} ^ 5$.

Or we could write it out using the following:

${a}^{b} / {a}^{c} = {a}^{b - c}$

${x}^{4} / {x}^{9} = {x}^{4 - 9} = {x}^{-} 5$

We must also use this theory:

${a}^{-} b = \frac{1}{a} ^ b$

${x}^{-} 5 = \frac{1}{x} ^ 5$