# How do you rewrite 1/x^-2 with positive exponents?

Feb 7, 2015

As ${x}^{2}$

A negative exponent means that the thing is "under the dividing bar".

So $\frac{1}{x} ^ - 2$ should be written as $\frac{1}{\frac{1}{x} ^ 2}$

And then use the rule of "dividing by a ratio is multiplying by its inverse"

OR:
We could say that every time we change $x$'s from above the bar to below, or the other way around, we change the sign.

So $\frac{1}{x} = \frac{1}{x} ^ \left(+ 1\right) = {x}^{-} \frac{1}{1} = {x}^{-} 1$ and vice versa.

So $\frac{1}{x} ^ \left(- 2\right) = {x}^{+ 2} / 1 = {x}^{2}$