Negative Exponents

A negative exponent means "take the reciprocal." So $x^{-n} = 1 / x^n$.

For example, $2^{-3} = 1 / 2^3 = 1 / 8$. Instead of multiplying 2 by itself, you divide by 2 repeatedly. Or you compute the positive power and flip it.

This definition keeps the quotient rule working: $x^2 / x^5 = x^{2-5} = x^{-3} = 1/x^3$. The pattern holds without exceptions.