Exponents and Order of Operations
- Exponents
Recall that multiplication is defined as repeated addition, for example
4 + 4 + 4 +
4 + 4 + 4 + 4 = 4 x 7
What about repeated multiplication? For example, is there an
easy way to write
4 x 4 x 4 x
4 x 4 x 4 x 4
Fortunately, mathematicians have developed a
convenient way of writing this. We write
4 x
4 x 4 x 4 x 4 x 4 x 4 = 47
Here, the number 4 is called the base
and the number 7 is called the exponent.
We read this as four to the seventh power.
Examples
Find the value of each expression
- 24
- 33
- 010
- 92
- 1221
- 109
Solutions
- 24 = 2 x 2 x 2 x 2
= 4 x 4 = 16
- 33 = 3 x 3 x3
= 9 x 3 = 27
- 010 = 0 x 0 x 0 x 0 x 0 x
0 x 0 x 0 x 0 x 0 = 0
- 92 = 9 x 9 =
81
- 1221 = 122
Notice that the 1 means the 122 only
appears one time
- 109 = 10 x 10 x 10 x 10 x
10 x 10 x 10 x 10 x 10 = 1,000,000,000
For any whole number b other than zero
b0
= 1
Example
160
= 1
- Order of Operations
Example
Consider the following expression
12 - 32
+ 2 x (5 + 1)
In what order should we work out this?
The general rule for working out arithmetic problems is that we work them
out in the following order:
- Inside parenthesis
- Exponents
- x and ÷
- + and -
If there are two operations of equal priority, we
work them out from right to left.
Example (Continued)
12 - 32
+ 2 x (5 + 1) = 12 - 32 + 2 x 6 Parentheses first: 5 + 1 = 6
= 12 - 9 + 2 x 6
Exponents next: 32 = 9
=
12 - 9 + 12
Multiplication next: 2 x 6 = 12
=
3 + 12
"-" and "+" are same so left first: 12 - 9
= 3
=
15
Exercises Calculate the following (To
check your answer hold mouse over the yellow rectangle)
(2 x 3)2 - 5 + 3 x 22
4 + 6 ÷ 2 x 5 - (32 + 1)
8 ÷ 4 x 3 + 1 - (40 - 1)
Back
to the Arithmetic of Whole Numbers page
Back
to the Math 187A page
Back to the Math
Department page
e-mail
Questions and Suggestions |