Understanding the Expression 15×15×15×15×0 15×15×15×15 and its Significance

In this article, we will explore the mathematical expression 15×15×15×15×0 15×15×15×15 and understand its evaluation using the order of operations. This expression is often used to illustrate the importance of the order of operations in mathematics. Let's break it down step by step.

The Order of Operations: A Primer

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure correct and consistent answers. The sequence is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This method ensures that expressions are evaluated correctly, leading to consistent and reliable results.

Evaluating the Expression: Step by Step

Let's evaluate the given expression 15×15×15×15×0 15×15×15×15 using the correct order of operations.

1. **Multiplication and Division:** We start with the multiplication operations first.

First, we evaluate the product 15×15×15×15×0. According to the properties of multiplication, any number multiplied by zero equals zero. Thus, 15×15×15×15×0 0. Next, we evaluate the product 15×15×15×15 50625 (15^4 50625).

2. **Addition and Subtraction:** Now, we perform the addition and subtraction operations as per the order of operations.

Combine the results from the multiplication operations:

(15×15×15×15×0) (15×15×15×15) 0 50625 50625.

Therefore, the final result of the expression 15×15×15×15×0 15×15×15×15 is 50625.

Breaking Down the Expression into Two Parts: A and B

We can also break down the given expression into two parts for easier understanding:

A 15×15×15×15×0 Since anything multiplied by 0 equals 0, A 0. B 15×15×15×15 This evaluates to 50625 as 15^4. A B A B 0 50625 50625.

Hence, the final result is 50625.

A Common Methodology in Algebra and Trigonometry

This method of evaluating expressions is a common practice in algebra and trigonometry. For example, in the context of Jerome E. Kaufmann's Algebra with Trigonometry for College Students Third Edition (1992, pp. 8-9), this expression would be used to illustrate the concept of the order of operations and the impact of multiplication by zero.

1. **Multiplication is done first:** The product on the left-hand side of the addition is zero, as anything multiplied by itself (in this case, by zero) is zero. Therefore, 15×15×15×15×0 0.

2. **The second four 15s when multiplied work out to 50625:** Thus, 15×15×15×15 50625.

3. **Adding the results:** Finally, combining these results gives us the final answer:

0 50625 50625.

By understanding and applying these principles, students can confidently solve similar expressions and develop a deeper understanding of mathematical operations.