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 Dependent Variable

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# Negative Integer Exponents

## Definition of a Negative Integer Exponent

You have seen how to work with exponents that are positive integers or 0.

Now, we will investigate exponents that are negative integers.

 Weâ€™ll begin with this expression: We can simplify the expression by canceling common factors. We can also simplify the expression by subtracting exponents.

Since simplifies to both and 2-3, we conclude .

This relationship holds in general.

Note:

Recall:

23 = 2 Â· 2 Â· 2

20 = 1

Definition â€” Negative Integer Exponent

Here, x 0 and n is a nonnegative integer.

Example 1

Find: 5-2

Solution

 Use the definition of a negative exponent:

So,

We can also define as follows:

Definition â€”

Here, x 0 and n is a nonnegative integer.

Example 2

a) Find:

b) Find:

Solution

 a. Use the definition b. Use the definition

Note:

A negative exponent does not determine if an expression is positive or negative. For example:

 positive negative