# 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
and
4 x 5 (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

 Powers have two parts; a base and an exponent. There are different ways of "saying" powers that you might hear: the fifth power of three three raised to the fifth power three to the power of five, or just three to the fifth

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.

## Exponents Worksheets

Try the worksheets below to practice working with exponents and bases.

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