Homework Help: Mathematics: Algebra: Negative Exponents of Fractions

To best understand this lesson, make sure that you have read and understand the following lessons:

1. Simplifying Negative Exponents
2. Simplifying Variables with Negative Exponents

This lesson will explain how to simplify the negative exponents in problems like the following two.

and

The first problem is simply a term with both negative and positive exponents. As you may have noticed in one of the previous lessons, the simplest form of the problem a^-2 is simply

The problem was simplified by just changing its exponent to the opposite sign (from negative to positive) and moving it to the bottom of a fraction.

The next problem we are simplifying has both negative and positive exponents. The variables with positive exponents are left alone while the variables with negative exponents are moved to the bottom of the fraction.

The next problem is already a fraction. The top and bottom both contain negative exponents. Since d^-3 on the bottom has a negative exponent, it is moved to the top of the fraction (numerator). Since the c^-3 on the top of the fraction has a negative exponent, it is moved to the bottom of the fraction (denominator).

The problem and work is shown below.

The next problem is a fraction with a negative exponent on top, but only positive exponents on the bottom:

The x^-2 on top of the fraction bar is moved below it, and its exponent is changed from negative two to positive two. Since there is already x² on the bottom, they are multiplied together. The number 1 is left on the top of the fraction because, as you may recall, when a term does not have an explicit coefficient, it has an implicit coefficient of 1.

Homework Help: Mathematics: Algebra

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