Writing Without Negatives

Simplified answers are usually written with positive exponents. So the last step of many problems is a rewrite: $x^{-4}$ becomes $\frac{1}{x^{4}}$. The rewrite also works the other way. When you want a single line without a fraction, $\frac{1}{x^{2}}$ can be written as $x^{-2}$.

Only the factor with the negative exponent moves. $5x^{-2}$ is $\frac{5}{x^{2}}$. The 5 has exponent 1, so it stays in the numerator. The exponent -2 belongs to the $x$ alone, because an exponent applies only to the base it is attached to.

For nonzero $a$, the negative exponent rule is $a^{-n} = \frac{1}{a^{n}}$. Use it in either direction, to remove a negative exponent or to write a fraction as a single power.