Math Example--Exponential Concepts--Laws of Exponents: Example 17

Topic

Exponents

Description

This example demonstrates the simplification of an expression involving multiplication and division with exponents. The problem involves simplifying (x² * x³) / x⁴, which results in x. This showcases how exponents behave when multiplying and dividing terms with the same base, illustrating the addition and subtraction of exponents in a single expression.

Understanding how to handle expressions with both multiplication and division of exponents is crucial in algebra and higher mathematics. These examples help students grasp the concept that when multiplying terms with the same base, exponents are added, and when dividing, they are subtracted. 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 multiplication and division with 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 example that combines multiplication and division with exponents: (x² * x³) / x⁴. Remember, we first multiply the terms in the numerator by adding their exponents: x² * x³ = x⁵. Then, we divide this result by x⁴, which means we subtract the exponents: x⁵ / x⁴ = x^{(5 - 4)} = x. Notice how the multiplication and division of exponents can sometimes simplify to a very basic expression. This is why it's so important to follow the order of operations and combine like terms when working with exponents!

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