Math Example--Exponential Concepts--Laws of Exponents: Example 6

Topic

Exponents

Description

This example focuses on simplifying an expression with both negative and positive exponents. The problem involves simplifying x^(-2) * x⁷ * x¹¹, which results in x¹⁶. This demonstrates how positive and negative exponents interact when multiplying terms with the same base, and how they can be combined to yield a single positive exponent.

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 interesting example with both negative and positive exponents: x^(-2) * x⁷ * x¹¹. Remember, when multiplying terms with the same base, we add the exponents, even if some are negative. So, we're adding -2, 7, and 11. What do we get? That's right, x^16. Notice how the negative and positive exponents combined to give us a positive result. This is a key concept when working with mixed exponents!

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