Math Example--Exponential Concepts--Laws of Exponents: Example 15

Topic

Exponents

Description

This example illustrates the simplification of an expression involving division with both positive and negative exponents. The problem involves simplifying x⁸ / x^(-4), which results in x¹². This demonstrates how positive and negative exponents interact when dividing terms with the same base, and how the result can yield a larger positive exponent.

Understanding how to handle expressions with mixed positive and 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 algebraically, considering 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 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: Now, let's look at an interesting example with both positive and negative exponents in division: x⁸ / x^(-4). Remember, when dividing terms with the same base, we subtract the exponents. But what happens when we subtract a negative exponent? It turns into addition! So, we're actually doing 8 - (-4), which is the same as 8 + 4. What do we get? That's right, x¹². Notice how dividing by a negative exponent actually increased our overall exponent. This is a powerful concept when working with mixed positive and negative exponents in division!

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