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Negative indices

A number can be raised to a negative index. It is the reciprocal of the number with the positive index.

\begin{align*} \Tblue{4}^{\Tred{-1}} &= \frac{1}{\Tblue{4}^\Torange{1}} = \frac{1}{4},\\ \Tblue{3}^{\Tred{-4}} &= \frac{1}{\Tblue{3}^\Torange{4}} = \frac{1}{81},\\ (\Tblue{-2})^{\Tred{-5}} &= \frac{1}{(\Tblue{-2})^\Torange{5}} = \frac{-1}{32}. \end{align*}