Math Lesson 7
Using Very Small and Very Large Numbers

Instruction 7-3

Estimate, Round Off, and Manipulate Very Small and Very Large Numbers | Percents and Their Interpretations | Positive Integer Powers of Non-negative Integers | Decimals, Fractions, Mixed Numbers, and Positive and Negative Integers on the Number Line | Summary

POSITIVE INTEGER POWERS OF NON-NEGATIVE INTEGERS 
CA GR5 NS 1.3.

Exponents

When working with exponents there are a few vocabulary words you need to know. Base is the number that is to be raised to a given exponent. An exponent is the number that tells how many times the base is used as a factor. The power is a number obtained by raising a base to an exponent. And finally, the standard form of a number is the usual or common way to write a number.

When you multiply a number by itself, you are raising a number by its power. To show that a number has been raised by a power, you use an exponent. For example, 5 x 5 x 5 means that the number 5 has been raised to the third power. The number of the exponent depends on the power that the number has been raised. The exponent also shows how many times the number is a factor.

For example, 5 x 5 x 5 is the same as 5³, meaning the base number five is raised to the power of three. So, 5³ =125 means that 5 x 5 x 5 = 125.

Any number to the second power is said to be squared. Any number to the third power is said to be cubed. With all exponents, you indicate that their base numbers a raised to certain powers.

For example:

● 7² means “seven to the second power,” which would be 49.
● 9³ means “nine to the third power,” which would be 729.
● 2²² means “two to the twenty-second power,” which would be 4194304.
● 12³ means “twelve to the third power,” which would be 1728.

But, what is the value of 6¹ and 6⁰?

You can use patterns to find the value of 6¹ and 6⁰?

6⁴ = 6 x 6 x 6 x 6
6³ = 6 x 6 x 6
6² = 6 x 6
6¹ = 6
6⁰ = 1

Any base raised to the exponent 1 equals the base. So, 6⁰ = 1

Any base raised to the exponent 0 equals the base. So, 6⁰ = 6

Worksheet 1 Word Problems

Worksheet 2 Rewrite Using a Base and Exponent  

Worksheet 3 Write into Expanded Form  

Worksheet 4 Write in the Standard Form 

Worksheet 5 Write in the Standard Form

Links for Students, Parents and Teachers

Now let's do Practice Exercise 7-3 (top). 

Next Page:  Decimals, Fractions, Mixed Numbers, and Positive and Negative Integers on the Number Line (top)