Math Example--Exponential Concepts--Laws of Exponents: Example 4

Topic

Exponents

Description

This example focuses on simplifying an expression with two negative exponents, resulting in a fraction. The problem involves simplifying x^(-10) * x^(-7), which results in x^(-17) or 1/x¹⁷. This demonstrates how negative exponents combine and how the result can be expressed as a fraction with a positive exponent.

Understanding how to handle multiple negative exponents is crucial in algebra and higher mathematics. These examples help students grasp the concept that when multiplying terms with negative exponents, the exponents are added, and the result can often be expressed as a fraction. 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 and their interactions. 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 two negative exponents: x^(-10) * x^(-7). Remember, we add the exponents when multiplying terms with the same base, even if they're negative. So, what do we get? x^(-17), right? But how can we express this in a more familiar form? It's equal to 1/x¹⁷. Notice how we've moved the negative exponent to the denominator and made it positive. This is a powerful technique when working with negative exponents!

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