**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 = 4^{7}
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
- 2
^{4 } - 3
^{3 } - 0
^{10 } - 9
^{2 } - 122
^{1 } - 10
^{9}^{ }
Solutions
- 2
^{4}= 2 x 2 x 2 x 2 = 4 x 4 = 16
- 3
^{3}= 3 x 3 x3 = 9 x 3 = 27
- 0
^{10}= 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 x 0 = 0
- 9
^{2}= 9 x 9 = 81
- 122
^{1}= 122 Notice that the 1 means the 122 only appears one time
- 10
^{9}= 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
**b**^{0}= 1
**Example**
16^{0}= 1
- 2
**Order of Operations**Consider the following expression
Example
12 - 3^{2}+ 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 - 3^{2}+ 2 x (5 + 1) = 12 - 3^{2}+ 2 x 6 Parentheses first: 5 + 1 = 6
= 12 - 9 + 2 x 6 Exponents next: 3^{2}= 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 2^{2 }^{ }4 + 6 ÷ 2 x 5 - (3 ^{2}+ 1)
8 ÷ 4 x 3 + 1 - (4 ^{0}- 1)
- Inside parenthesis
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