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Properties of Exponents
You have seen the basic principles for addition and multiplication of real numbers. From these basic principles, other principles can be derived. Note some properties of exponents that follow easily from the basic principles.

Notice, for example, that

22 - 23 = (2 - 2) - (2 - 2 - 2)

= 4 - 8

= 32

and that 25 = 2 - 2 - 2 - 2 - 2 = 32

In fact, it is easy to prove the following principle:

x x2 - x3 = x5

This principle tells you that for each real number 'x', the product of 'x2' by 'x3' is 'x5'. [Notice that 2 + 3 = 5.]

Note also, for example, that

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These examples suggest the following principles that are easily proved to be consequences of the basic principles:

[Notice that 5 - 2 = 3.]

The principles suggest methods you may use to solve problems like the following without using pencil and paper:

You may, of course, check the answers by computing. For example, in the last problem we have:

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Real Numbers

Formulas, Functions, Graphs

Linear Functions

Quadratic Functions

Functions of Higher Degree

Properties of Exponents

Products and Factoring

Quadratic Equations

Solving Problems

Algebra Fundamentals