Powers (Bases and Exponents)
You've probably already seen that in math there are different ways of writing the same thing:
4 + 4 + 4 + 4 + 4 + 4
(repeated addition)
and
4 x 6 (multiplication)
Multiplication is a shorter and neater way of showing repeated addition.
Powers: Bases and Exponents
In a similar way to how multiplication can be used in place of repeated addition, Powers can be used to show repeated multiplication.
3 x 3 x 3 x 3 x 3 (repeated multiplication)
and
35 (Power)
New Words and Terms To Learn
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Powers have two parts; a base and an exponent. There are different ways of "saying" powers that you might hear:
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Memory Hint: base is on the bottom - like most bases!
Examples with bases and exponents
The examples below will help with understanding how values, bases, exponents, powers, and repeated multiplication are related.
| Power | Base | Exponent | Repeated Multiplication | Value |
| 43 | 4 | 3 | 4 x 4 x 4 | 64 |
| 35 | 3 | 5 | 3 x 3 x 3 x 3 x 3 | 243 |
| 26 | 2 | 6 | 2 x 2 x 2 x 2 x 2 x 2 | 64 |
| 54 | 5 | 4 | 5 x 5 x 5 x 5 | 625 |
| 73 | 7 | 3 | 7 x 7 x 7 | 343 |
Repeated Multiplication
Power
|
Multiplication | ||
35
|
3 x 3 x 3 x 3 x 3 | ||
| Multiply in steps - do two bases at
a time. Multiply the products by the remaining bases. |
3 x 3 = 9 | 3 x 3 = 9 | x 3 |
| 9 x 9 = 81 | x 3 | ||
| 81 x 3 = 243 | |||
Note: There are always different combinations of multiplication that produce the same answer. |
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Exponents Worksheets
Try the worksheets below to practice working with exponents and bases.
Writing
and Identifying Bases and Exponents