The Art of Interface

Article 11 — Appendix A.24

^ — power function

Category. Mathematics.

Abstract. Power: definition, plot, properties and identities.

Reference. This article is a part of Librow scientific formula calculator project.

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1. Definition

Power function is the function of kind

xa

2. Plot

Power function domain depends on power a, but it is always defined for positive real half-axis (0, +∞). Parabola plot for a = 2 is depicted below — fig. 1.

Fig. 1. Plot of the power function y = x^2. Fig. 1. Plot of the power function y = x2.

Function codomain as well depends on power a, but it always includes positive half of the real axis (0, +∞).

3. Identities

Negative power:

x−a = 1 /xa

Power sum and difference:

xa + b = xa xb
xa − b = xa/xb

Power product:

xab = (xa)b

4. Support

Power function ^ of the real argument is supported by free version of the Librow calculator.

Power function ^ of the complex argument is supported by professional version of the Librow calculator.

5. How to use

To calculate power of the number:

9^2;

To calculate power of the current result:

rslt^2;

To engage the current result as power:

9^rslt;

To calculate power of the number x in memory:

mem[x]^2;

To engage number x in memory as power:

9^mem[x];