Math Example--Exponential Concepts--Laws of Exponents: Example 9

Topic

Exponents

Description

This example demonstrates the simplification of an expression with multiple negative exponents and one positive exponent. The problem involves simplifying x^(-6) * x^(-5) * x⁷, which results in x^(-4) or 1/x⁴. This showcases how positive and negative exponents interact when multiplying terms with the same base, and how the result can be expressed as a fraction.

Understanding how to handle expressions with mixed positive and negative exponents is crucial in algebra and higher mathematics. These examples help students grasp the concept that when multiplying terms with the same base, the exponents are added algebraically, regardless of their signs. 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 positive and 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 multiple negative exponents and one positive exponent: x^(-6) * x^(-5) * x⁷. Remember, when multiplying terms with the same base, we add the exponents, even if some are negative. So, we're adding -6, -5, and 7. What do we get? That's right, x^(-4). But how can we express this in a more familiar form? It's equal to 1/x⁴. Notice how we've moved the negative exponent to the denominator and made it positive. This is a key concept 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.