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

What should you do with negative exponents?

1. Leave them as they are

2. Express them as fractions

3. Add a positive value

4. Ignore them

The correct answer is: Express them as fractions

When encountering negative exponents, the correct approach is to express them as fractions. A negative exponent indicates that the base should be taken as the reciprocal. For example, if you have a term like \( a^{-n} \), it can be rewritten as \( \frac{1}{a^n} \). By converting negative exponents into fractions, you make the expression easier to interpret and work with in calculations. This is a standard mathematical convention, and using fractions for negative exponents helps maintain clarity and consistency in mathematical expressions. Other approaches, such as leaving them unchanged, adding a positive value, or ignoring them, do not follow established mathematical rules for handling exponents. This could lead to confusion and incorrect results. Therefore, expressing negative exponents as fractions is the proper and meaningful way to handle them in mathematical contexts.