The Helpful Mathematics
+38 044 572 93 47

Article 11 — Appendix A.24

^ — power function

Category. Mathematics.

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

References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products.

1. Definition

Power function is the function of kind

xa

2. Graph

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

Fig. 1. Graph of the power function y = x^2 Fig. 1. Graph 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 ^ is supported in:

Power function of the complex argument ^ is supported in:

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];