Math Example--Exponential Concepts--Laws of Exponents: Example 14

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving division with negative exponents. The problem involves simplifying x^(-5) / x⁶, which results in x^(-11) or 1/x¹¹. This showcases how negative and positive 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 division 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 dealing with negative exponents. 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 involving division with negative exponents: x^(-5) / x⁶. Remember, when dividing terms with the same base, we subtract the exponents. So, we're subtracting 6 from -5. What do we get? That's right, x^(-11). But how can we express this in a more familiar form? It's equal to 1/x¹¹. Notice how the negative exponent in the numerator and the positive exponent in the denominator combined to give us a larger negative exponent. This is a key concept when working with negative exponents in division!

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