Math Example--Exponential Concepts--Laws of Exponents: Example 16

Topic

Exponents

Description

This example focuses on simplifying an expression with negative exponents in both the numerator and denominator. The problem involves simplifying x^(-7) / x^(-5), which results in x^(-2) or 1/x². This demonstrates how negative exponents interact when dividing terms with the same base, and how the result can be expressed as a fraction.

Understanding how to handle expressions with negative exponents in both numerator and denominator is crucial in algebra and higher mathematics. These examples help students grasp the concept that when dividing terms with the same base, the exponents are subtracted, even when both are negative. 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 negative exponents in division. 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 example with negative exponents in both the numerator and denominator: x^(-7) / x^(-5). Remember, when dividing terms with the same base, we subtract the exponents. So, we're subtracting -5 from -7. What do we get? That's right, x^(-2). But how can we express this in a more familiar form? It's equal to 1/x². Notice how subtracting a negative exponent is the same as adding its positive value. This is a key concept when working with negative exponents in both numerator and denominator!

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