Math Example--Exponential Concepts--Laws of Exponents: Example 11

Topic

Exponents

Description

This example demonstrates the simplification of an expression with both positive and negative exponents, including a zero exponent. The problem involves simplifying x^(-10) * x¹⁰ * x^(-2), which results in x^(-2) or 1/x². This showcases how positive and negative exponents interact when multiplying terms with the same base, and how zero exponents affect the result.

Understanding how to handle expressions with mixed positive and negative exponents, including zero 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, including zero 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 interesting example with both positive and negative exponents, including a zero exponent: x^(-10) * x¹⁰ * x^(-2). Remember, when multiplying terms with the same base, we add the exponents, even if some are negative. So, we're adding -10, 10, and -2. What do we get? That's right, x^(-2). Notice how the positive and negative 10 exponents canceled each other out. How can we express this result in a more familiar form? It's equal to 1/x². This example shows how important it is to carefully combine all exponents, even when some of them cancel out!

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