Introduction to Exponents

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Videos, worksheets, stories and songs to help Grade 6 students learn what is the meaning of exponents.

In this lesson we will learn

  • the basic meaning of exponents that are whole numbers
  • how to evaluate and simplify expressions with exponents

Exponent is a shortcut for showing repeated multiplication.
For example, 25 = 2 × 2 × 2 × 2 × 2 = 32
2 is called the base and 5 is called the exponent.
25 can be read as “2 raised to the fifth power” or “2 raise to the power 5” or “2 raised by the exponent of 5” or “2 to the 5”.

If the exponent is 0 then the answer is always 1.
For example, 90 = 1, 210 = 1
Some mathematicians define 00 = 1, whereas others leave it undefined.

The following diagram shows how to calculate exponents or indices. Scroll down the page for more examples and solutions on exponents.

Basic exponents

Power and Exponent
A Power consists of two parts, Exponent and Base, We are going to learn how to identify the components of a Power and to evaluate it if necessary.

Exponent Song
A power’s what you get when you multiply a number by itself one or more times
To give you an example let’s look at powers of the number 5

5 times 5 is 25
5 times 5 times 5 is 125
5 times 5 times 5 times 5 is 625

There’s two parts of a power, a base and an exponent.
The base is on the bottom it’s the number being multiplied
The exponent’s on the top it tells you how many times the base is multiplied by
Where’s the base? The base is on the bottom!
Where’s the exponent? The exponent’s on the top!

5 times 5 is 25
5 times 5 times 5 is 125
5 times 5 times 5 times 5 is 625

Now let’s look at the 3 different forms of exponents, you might find that you already know them
2 to the 3 is known as the exponent form, it’s because there’s an exponent in there
2 x 2 x 2 is the expanded form, it’s because you’ve expanded the exponent form
And the result of 8 is the standard form, a plain number is the standard

Song and video by Colin Dodds.

Exponents - Basics
Covers the basic meaning of exponents that are whole numbers and how to evaluate and simplify expressions. Also defines zero exponent.
By definition b0 = 1

Intro to Exponents
Clarifying terminology of math: exponents.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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