Powers (Bases and Exponents)

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You've probably already seen that in math there are different ways of writing the same thing:

4 + 4 + 4 + 4 + 4
(repeated addition)
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
3
5 (Power)

New Words and Terms To Learn

Annotated illustration of 3 to the 5th power

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
434 3 4 x 4 x 4 64
353 5 3 x 3 x 3 x 3 x 3 243
262 6 2 x 2 x 2 x 2 x 2 x 2 64
545 4 5 x 5 x 5 x 5 625
737 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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