EL032 Algebra Basics: Rational Exponents and Radicals

What does 3 raised to the power 2/5 mean? Definitions, Rules, and Examples for manipulating rational #exponents and #radicals A basic #algebrareview for college and #highschool students. Subscribe @Shahriari for more math videos, mostly at the college level.

00:00 Introduction
02:41 The meaning of x^{1/2}, x^{1/3}, and more generally x^{1/n}
05:05 Arbitrary fractions as exponents? What is the difference between x^{3/4} and x^{4/3}?
06:52 Square root of 9 is 3 and not plus or minus 3, what is the square root of x^2?
09:20 Rules for manipulating exponents
10:21 How do you remember the rules?
12:21 Examples of manipulating radicals and exponents
14:49 A cautionary tale: if the x in x^a is negative, then the exponent rules may fail
17:39 Graphs of Exponential functions modeling exponential growth and decay
19:44 Irrational exponents. What does 2^{sqrt(2)} could possibly mean?

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.