Introduction to Exponents

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.

 

Calculating with Negative Bases:
When the base is negative, the sign of the result depends on whether the exponent is even or odd:

• Negative base raised to an even exponent: The result is positive. For example, ((-2)⁴ = (-2) × (-2) × (-2) × (-2) = 16).
• Negative base raised to an odd exponent: The result is negative. For example, ((-3)³ = (-3) × (-3) × (-3) = -27).

Exponent Worksheets
Practice your skills with the following exponent worksheets:
Printable & Online Exponent Worksheets

In this lesson, we will only look at exponents that are whole numbers. It also possible for exponents to be negative or be fractions. Check out the following lessons:
More Lessons on Exponents

Basic exponents
Examples:
2³ =
3² =
(-4)² =
(-4)³ =
(-1)¹ =
(-1)² =
(-1)³ =
5³=
(-5)³⁼

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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.
Examples:
2⁴ =
5² =
(-3)³ =
-3³ =
x² =
-2³ =
6² =
(-4)² =
12² =
y³ =
3a² =
(-x)² =
-4c² =
xy^{3 =}

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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.

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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

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Intro to Exponents
Clarifying terminology of math: exponents.

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Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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