### Calculator/Geometry Strategies for Understanding Properties of x^(m/n)

John J. Edgell, Jr.

Professor Mathematics

Southwest Texas State University

601 University Drive

San Marcos, Texas 78666

Phone: (512) 245-2551

Fax: (512) 245-3425

#### ABSTRACT

Some students may benefit in the understanding and applying real
numbers of the form x^(m/n) from a combination of calculator and
theoretical geometric techniques. The poster/paper will demonstrate
a seven-step calculator routine for expressing x^(m/n) and a spiral
sequence of similar right trigons for conceptualizing x^(m/n).
Further calculator routines and trigonal spirals will demonstrate
properties relating x^(m/n) and x^(M/N). Analysis of such trigonal
spirals will reveal strategies for exploring comparisons of x^(m/n) and
x^(M/N). Finally, a summary analysis for the theoretical foundations of
each spiral will be included.