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Proposition: Calculation Rules for General Powers
Let \(x,y\) be real numbers and let \(a,b\) be positive real numbers. Then the general power function obeys the following calculation rules:
\[\begin{array}{rl}
(i)&a^{x+y}=a^x\cdot a^y,\\
(ii)&(a^x)^y=a^{x\cdot y},\\
(iii)&a^x\cdot b^x=(ab)^x,\\
(iv)&a^{-x}=\frac 1{a^x}.\\
\end{array}\]
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
