Lesson 8 Instruction, Page 1

Raising Numbers to Various Powers
CA GR7 NS 1.2, CA GR7 AF 2.1

When we multiply a number by itself we are raising it to a power. And in math we use an exponent to show that a number has been raised to a power. For example: 7 x 7 means that we have raised the number 7 to the second power.

Or 7 x 7 x 7 means that we have raised 7 to the third power. But instead of writing the number 7 over and over, we use exponents to show how many times the number is a factor.

An exponent is a small number to the right and above the factor. The number itself (the seven in this case) is called the base number.

For example, 7 x 7 is the same as 7², meaning the base number seven is raised to the second power. And 7 x 7 x 7 is the same as 7³, meaning the base number seven is raised to the third power.

So, 7² = 49 means that 7 x 7 = 49. Likewise, 7³ = 343 means that 7 x 7 x 7 = 343.

Any number to the second power is said to be squared (i.e. 7² is seven squared).

Any number to the third power is said to be cubed (i.e. 7³ is seven cubed).

With all other exponents, however, we just indicate that their base numbers are raised to certain powers.

For example:

6⁴ means "six to the fourth power," which would be 1296. Try it.
5⁵ means "five to the fifth power," which would be 3125. Try it.
4⁶ means "four to the sixth power," which would be 4096. Try it.
15⁴ means "fifteen to the fourth power," which would be 50,625. Try it.

But what about the base number with an exponent of one, like 14¹? Well, since an exponent indicates how many times the base number is a factor, the number 14 is a factor once, so 14¹ = 14, and any number to the power of one is the same as the number itself.

Now let's do Practice Exercise 8-1, Practice Exercise 8-1-a.

Next Page: Rules of Exponents