Multiplication and Division:
Introduction to Exponents
Remember, multiplication is the shortcut for doing repeated addition:
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54
6 × 9 = 54
Similarly, there is a shortcut to writing multiplication if you do the same thing over and over again:
2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
Here we multiplied 2 together 7 times.
For the shorthand, we write \(2^{7}\) = 128
That little 7 means the number of times that we multiply 2 by itself and is called an exponent; sometimes we call it a power. Here are a couple more examples:
\(5^{3}\)=5 × 5 × 5 = 125
\(7^{2}\) = 7 × 7 = 49
\(2^{4}\) = 2 × 2 × 2 × 2 = 16
Some of the easiest to calculate are the powers of 10. Try these:
\(10^{2}\) = 100
\(10^{4}\) = 10,000
\(10^{8}\) = 100,000,000
Notice a pattern?
Scripture Connection
Alma 37:6
Like the small and simple things in this scripture, exponents also bring about great things. They are tiny numbers that make a big difference on the outcome of the answer.
Video Source (02:36 mins) | Transcript
When solving problems with exponents, write out the problem and do the multiplication one step at a time, as shown in the video:
Video Source (02:29 mins) | Transcript
Additional Resources
- Khan Academy: Introduction to Exponents (03:02 mins, Transcript)
Practice Problems
Evaluate the following expression:
- \(1^{2}\) = ?
- \(8^{2}\) = ?
- \(0^{3}\) = ?
- \(5^{3}\) = ?
- \(4^{3}\) = ?
- \(3^{4}\) = ?
