Math Example--Exponential Concepts--Laws of Exponents: Example 21

Topic

Exponents

Description

This example focuses on simplifying an expression involving multiplication and division with negative exponents. The problem involves simplifying (x^(-3) * x^(-5)) / x⁵, which results in 1/x¹³. This demonstrates how negative exponents interact when multiplying and dividing terms with the same base, and how the result can be expressed as a fraction with a positive exponent in the denominator.

Understanding how to handle expressions with negative exponents in both multiplication and division is crucial in algebra and higher mathematics. These examples help students grasp the concept that when multiplying terms with the same base, exponents are added, and when dividing, they are subtracted, even when dealing with negative exponents. By presenting various scenarios, students learn to apply these rules confidently in different mathematical contexts.

Exposure to multiple worked-out examples is essential for students to fully comprehend the concept of combining multiplication and division with negative exponents. Each example builds upon previous knowledge, reinforcing core principles while introducing new complexities. This approach helps students develop a deeper understanding and the ability to tackle more challenging problems involving exponents.

Teacher's Script: Now, let's look at an example with negative exponents in both multiplication and division: (x^(-3) * x^(-5)) / x⁵. First, let's multiply the terms in the numerator by adding their exponents: x^(-3) * x^(-5) = x^(-8). Now, we divide this result by x⁵, which means we subtract the exponents: x^(-8) / x⁵ = x^{(-8 - 5)} = x^(-13). How can we express this in a more familiar form? It's equal to 1/x¹³. Notice how the negative exponents in the numerator and the positive exponent in the denominator combined to give us a larger negative exponent. This is a key concept when working with negative exponents in both multiplication and division!

For a complete collection of math examples related to Exponents click on this link: Math Examples: Laws of Exponents Collection.