Power (Algebra)/Integer/Examples/Minus 3 to the Power of Minus 3
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Example of Integer Power
- $-3^{-3} = -\dfrac 1 {27}$
Proof
| \(\ds -3^{-3}\) | \(=\) | \(\ds \paren {-\dfrac 1 3}^3\) | Definition of Integer Power | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {\paren {-3}^3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {-27}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\dfrac 1 {27}\) |
$\blacksquare$
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: Exercise $3$