- Factors
- Exponential Notation

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.

- Factors
- Exponential Notation

Let’s begin our review of arithmetic by recalling the meaning of multiplication for whole numbers (the counting numbers and zero).

Multiplication is a description of repeated addition.

In the addition

the number 7 is repeated as an *addend** 4 *times.* Therefore, we say we have *four times seven* and describe it by writing

The raised dot between the numbers 4 and 7 indicates multiplication. The dot directs us to multiply the two numbers that it separates. In algebra, the dot is preferred over the symbol

In a multiplication, the numbers being multiplied are called *factors.* The result of a multiplication is called the *product.* For example, in the multiplication

the numbers 4 and 7 are factors, and the number 28 is the product. We say that 4 and 7 are factors of 28. (They are not the only factors of 28. Can you think of others?)

Now we know that

This indicates that a first number is a factor of a second number if the first number divides into the second number with no remainder. For example, since

both 4 and 7 are factors of 28 since both 4 and 7 divide into 28 with no remainder.

Quite often, a particular number will be repeated as a factor in a multiplication. For example, in the multiplication

the number 7 is repeated as a factor 4 times. We describe this by writing

The repeated factor is the lower number (the base), and the number recording how many times the factor is repeated is the higher number (the superscript). The superscript number is called an *exponent.*

An exponent is a number that records how many times the number to which it is attached occurs as a factor in a multiplication.

For Examples 1, 2, and 3, express each product using exponents.

Then we have

Expand

Expand

For the following problems, express each product using exponents.

Suppose that the letters

Suppose that the letters

For the following problems, expand each product (do not compute the actual value).

For the following problems, specify all the whole number factors of each number. For example, the complete set of whole number factors of 6 is 1, 2, 3, 6.

20

14

12

30

21

45

11

17

19

2

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