The Art of Interface

^ — power function

Category. Mathematics.

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

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 = x2.

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

3. Identities

Negative power:

xa = 1 /xa

Power sum and difference:

xa + b = xa xb
xab = 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];``