This tutorial: Part A: Integer Exponents
|
If a is a real number and n is a positive integer, then by an we mean the quantity
The number a is called the base and the number n is called the exponent.
Thus, a1 = a, a2 = a.a, a5 = a.a.a.a.a
Here are some examples with actual numbers:
The following rules show how to combine such expressions.
|
Caution
|
Fill in the missing exponents and other numbers and press "Check.". (Raised boxes are exponents.)
Negative and Zero Exponents
It turns out to be very useful to allow ourselves to use exponents that are not positive integers. These are dealt with by the following definition.
Negative and Zero Exponents If a is any real number other than zero and n is any positive integer, then we define
Examples
|
Here are some for you to try.
We can use the exponent identities to convert between the two forms just described:
You should go over Part B in the next tutorial before trying the examples and exercises in Section 0.2 of the Algebra Review of Applied Calculus and Finite Mathematics and Applied Calculus
An expression of rational form is an expression written as a ratio:
bxn where m and n ≥ 0.
Examples: Expressions in Rational Form:
2x4,
7x4,
2.3,
7
but
7is not in rational form because the exponent of x is negative.
An expression of exponential form is an expression written as axn where n is any exponent (possibly negative or zero).
Examples: Expressions in Exponential Form:
4.1x-3
,
3x2
,
5.1x-4
,
7
but
7x-4is not in exponential form because of the x is in the denominator.
Copyright © 2007 Stefan Waner