Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the purpose of switching the fraction in a negative exponent?

1. To simplify the fraction

2. To make the calculations easier

3. To convert it to a positive exponent

4. To change the value of the fraction

The correct answer is: To convert it to a positive exponent

When working with negative exponents, switching the fraction serves to convert it to a positive exponent. This is based on the mathematical rule that states that \(a^{-n} = \frac{1}{a^n}\). In other words, a negative exponent indicates that you take the reciprocal of the base and then apply the positive exponent to it. For example, if you have \(x^{-2}\), it can be rewritten as \(\frac{1}{x^2}\). This transformation makes it easier to work with the expression in various mathematical contexts, such as simplifying equations or performing calculations. The conversion from a negative to a positive exponent is crucial for applying further mathematical operations correctly. This process does not change the value of the fraction, merely its representation, and does not directly simplify the fraction itself; therefore, those aspects are secondary to the main purpose of converting the exponent. The key takeaway is that the primary function of switching the fraction in the context of negative exponents is to allow for clearer mathematical operations by turning the negative exponent into a positive one.