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Proposition: General Powers of Positive Numbers
Let \(x\) be any real number and let \(a > 0 \) be a positive real number. Then the general power function \(a\to a^x\) is welldefined and equals the exponential function of general base \(a\), formally:
\[a^x=\exp_a(x).\]
The following interactive figure demonstrates the general power in relation to different values of exponents \(x\in[20,20]\).
Table of Contents
Proofs: 1
 Proposition: Calculation Rules for General Powers
 Proposition: Derivative of General Powers of Positive Numbers
 Proposition: Integral of General Powers
Mentioned in:
Corollaries: 1
Lemmas: 2
Proofs: 3 4 5
Propositions: 6 7 8 9 10 11 12 13
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983