Power (Algebra)/Rational Number/Examples/0.125 to the Power of Minus Two Thirds
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Example of Rational Power
- $0 \cdotp 125^{-2/3} = 4$
Proof
\(\ds 0 \cdotp 125^{-2/3}\) | \(=\) | \(\ds \paren {\dfrac 1 8}^{-2/3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 8^{2/3}\) | Definition of Rational Power | |||||||||||
\(\ds \) | \(=\) | \(\ds 64^{1/3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt [3] {64}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4\) |
$\blacksquare$
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 $4$