Math Example--Exponential Concepts--Laws of Exponents: Example 24

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with negative exponents. The problem involves simplifying (x^(-2) * x^(-6)) / x^(-8), which results in 1. This showcases how negative exponents interact when multiplying and dividing terms with the same base, and how they can cancel out to yield a result of 1.

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: Let's look at an interesting example with all negative exponents: (x^(-2) * x^(-6)) / x^(-8). First, let's multiply the terms in the numerator by adding their exponents: x^(-2) * x^(-6) = x^(-8). Now, we divide this result by x^(-8). Remember, when dividing terms with the same base, we subtract the exponents. So, x^(-8) / x^(-8) = x^{(-8 - (-8))} = x⁰ = 1. This example shows us something fascinating: when we have the same base with the same exponent in both numerator and denominator, they cancel out completely, leaving us with 1. This is a powerful concept that can help simplify complex expressions!

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