Homework Help: Mathematics: Algebra: Negative Exponents of Numbers

Exponents are superscript numbers (a small number written near the top of another number) which show how many times a number or a variable is multiplied by itself. Before continuing through this lesson, you should make sure that you have read and understand the following three lessons on exponents:

1. Simplifying Exponents of Numbers
2. Simplifying Exponents of Variables
3. Simplifying Exponents of Polynomials

As you know a negative is the opposite of positive. You also know that multiplication is the opposite of division. So far, we have been dealing with positive exponents which show how many times the number 1 is multiplied by a given number. Negative exponents indicate the inverse of the corresponding positive exponent.

Take a look at the example below:

5²
1 * 5 * 5
25

To find what 5 to the second power is you simply multiply 1 by the number 5 two times. Now to, find what 5 to the negative second power is, take inverse of 5².

5^-2
5² = 1 * 5 * 5 = 25
5^-2 = 1 / 25 = 0.04

Since a fraction is really just a division problem shown in a different way, the work to our problem [5^-2] can be shown in a fraction as below:

The answer can be left as a simplified fraction (in the above problem this would be 1/25) or as a decimal (in the above problem .04).

Homework Help: Mathematics: Algebra

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