Math Example--Exponential Concepts--Laws of Exponents: Example 10

Topic

Exponents

Description

This example focuses on simplifying an expression with both positive and negative exponents. The problem involves simplifying x³ * x^(-5) * x^(-3), which results in x^(-5) or 1/x⁵. This demonstrates 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: Let's look at another example with both positive and negative exponents: x³ * x^(-5) * x^(-3). Remember our rule: when multiplying terms with the same base, we add the exponents, even if some are negative. So, we're adding 3, -5, and -3. What do we get? That's right, x^(-5). But how can we express this in a more familiar form? It's equal to 1/x⁵. 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.