Negative Means Reciprocal

Now take the quotient rule one step past zero. In $\frac{x^{2}}{x^{5}}$, two factors of $x$ cancel from the top and the bottom, and three factors of $x$ are left in the denominator: $\frac{1}{x^{3}}$. The quotient rule says to subtract the exponents, $2-5 = -3$, so the same expression is $x^{-3}$. The two results must be equal, so $x^{-3} = \frac{1}{x^{3}}$.

A negative exponent means a reciprocal. For example, $2^{-3} = \frac{1}{2^{3}} = \frac{1}{8}$. It does not mean that the value is negative.

You can also see it as a pattern. Each time the exponent of 2 goes down by 1, the value is divided by 2: $2^{3} = 8$, $2^{2} = 4$, $2^{1} = 2$. Continuing the pattern gives $2^{0} = 1$, then $2^{-1} = \frac{1}{2}$, $2^{-2} = \frac{1}{4}$ and $2^{-3} = \frac{1}{8}$.