Powers
When the same number is multiplied by itself again and again, it is called
repeated multiplication.
Example
In the following charts, the numbers 3 and 4 are multiplied by
themselves.
Multiplication
Answer
Multiplication
Answer
3×3
9
4×4
16
3×3×3
27
4×4×4
64
3×3×3×3
81
4×4×4×4
256
Another way of writing repeated multiplication is by using powers.
What is a power?
A power is an abbreviated (short) way of writing a number.
A power looks like:
Power
2
4
Exponent
Base
42 means that 4 is multiplied by itself 2 times.
42 = 4 × 4 = 16
Each part of the power has a special name.
The BASE is the number that will be multiplied by itself again and again.
The EXPONENT represents the number of bases to be multiplied.
The POWER refers to the base and exponent written as shown above.
Power is also known as the exponential form of a number.
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Placing powers into the tables we worked with earlier provides a better understanding of
what powers represent.
Repeated
Multiplication
3×3
Power
Answer
32
9
33
27
4
81
Power
Answer
42
16
3
3×3×3
3×3×3×3
3
Repeated
Multiplication
4×4
4×4×4
4
64
4×4×4×4
44
256
There are names for commonly used exponents.
Power
Exponent
Name
Examples
42
2
squared
62 , 92
43
3
cubed
63 , 93
42 can be expressed four ways:
four to the second power
or
four squared
or
four exponent two
or
four to the power of two
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Think About …
Find examples of numbers with exponents in your science text book, other
science reference book or on the Internet.
What would the numbers look like if they were written out?
Why do you think they are written with exponents?
Practice: Working with Powers
1. Review powers by completing the chart below.
Power
Repeated
Multiplication
Answer
52
5×5
25
6×6×6
103
45
3×3×3×3
102
152
7×7×7
83
9×9
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Mathematics
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Powers
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