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

What is the method for dividing exponential expressions?

1. Add the exponents

2. Subtract the exponents

3. Multiply the exponents

4. Divide the bases

The correct answer is: Subtract the exponents

When dividing exponential expressions that have the same base, the method involves subtracting the exponents. This rule can be stated as follows: for any non-zero number \( a \) and integers \( m \) and \( n \), \[ \frac{a^m}{a^n} = a^{m-n}. \] This means that to divide two powers with the same base, you take the exponent of the numerator and subtract the exponent of the denominator. For instance, if you have \( \frac{x^5}{x^2} \), you would subtract the exponents (5 - 2), leading to \( x^{5-2} = x^3 \). Understanding this rule is crucial for simplifying expressions in algebra and helps maintain the integrity of the mathematical operation when manipulating polynomial and exponential forms. This subtraction method is consistently used in various problems involving exponential fractions, making it a foundational concept in algebra.