Raising Numbers to Various Powers | Roots & Radicals | Signed Numbers & Roots | Rational & Irrational Numbers | Real & Imaginary Numbers | Finding Square Roots & Other Roots | Summary 

Raising Numbers to Various Powers

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 x7 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. And, 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 a 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 lets do Practice Exercise 8-1

Next Page: Roots and Radicals