Solve (4²•2-⁴) • (5²•3-³): Step-by-Step Solution

Hey there, math enthusiasts! Today, we're diving deep into a fascinating mathematical expression: (4²•2-⁴) • (5²•3-³). Sounds intimidating? Don't worry, we'll break it down step by step, making sure everyone, from math newbies to seasoned pros, can follow along. Our mission is not just to solve it, but to truly understand the underlying concepts. So, grab your pencils, open your minds, and let's embark on this mathematical journey together! We'll start by unraveling the order of operations and then explore each component of the expression in detail. By the end of this article, you'll not only have the answer but also a solid grasp of how we got there. Remember, mathematics is a journey, not a destination, and every step we take enhances our problem-solving skills and logical thinking. So, let's put on our thinking caps and get started!

Understanding the Order of Operations

Before we even think about numbers, let's quickly revisit the golden rule of mathematical expressions: the order of operations. You might have heard of the acronym PEMDAS or BODMAS. It stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is our roadmap, ensuring we solve the expression in the correct sequence. Think of it like a recipe; if you mix the ingredients in the wrong order, you might not get the desired result! So, when we look at (4²•2-⁴) • (5²•3-³), we know we need to tackle the exponents first, then the multiplication, and finally the subtraction within the parentheses. The multiplication between the two parenthetical expressions comes last. Sticking to this order is crucial for arriving at the correct answer. It's like building a house; you need a solid foundation before you can put up the walls. Understanding and applying the order of operations is the cornerstone of mathematical accuracy. This principle ensures that everyone solving the same problem arrives at the same answer, which is the beauty and consistency of mathematics. Let's keep this in mind as we dissect our expression further.

Unpacking the First Expression: (4²•2-⁴)

Let's zoom in on the first part of our problem: (4²•2-⁴). The first thing we spot is the exponent, 4². Remember, this means 4 multiplied by itself, which is 4 * 4 = 16. So, we can rewrite our expression as (16•2-⁴). Now, we have multiplication and subtraction. According to PEMDAS/BODMAS, multiplication comes before subtraction. So, we multiply 16 by 2, which gives us 32. Our expression now looks like this: (32-⁴). Finally, we subtract 4 from 32, resulting in 28. So, the value of the first expression, (4²•2-⁴), is 28. See how breaking it down step by step makes it much less daunting? It's like reading a long book; you tackle it chapter by chapter. Each step we take brings us closer to the final solution. This meticulous approach not only helps us avoid errors but also deepens our understanding of the mathematical processes involved. Understanding each step and its rationale is the key to mastering mathematics. Let's carry this understanding forward as we tackle the second expression.

Decoding the Second Expression: (5²•3-³)

Now, let's turn our attention to the second part of the expression: (5²•3-³). Just like before, we start with the exponent, 5². This means 5 multiplied by itself, which is 5 * 5 = 25. So, we can rewrite our expression as (25•3-³). Next, we have multiplication and subtraction. Following the order of operations, we perform the multiplication first. 25 multiplied by 3 equals 75. Our expression now reads (75-³). Finally, we subtract 3 from 75, which gives us 72. So, the value of the second expression, (5²•3-³), is 72. Just like with the first expression, breaking it down into smaller steps made it much easier to solve. It’s like solving a puzzle; you fit the pieces together one by one until the whole picture becomes clear. This step-by-step approach is a powerful tool in mathematics, allowing us to tackle even the most complex problems with confidence. Each step is a building block, contributing to the final solution. Now that we've solved both expressions within the parentheses, we're ready to bring them together and complete the final step.

Bringing It All Together: The Final Calculation

We've successfully dissected both parts of our expression. We found that (4²•2-⁴) = 28 and (5²•3-³) = 72. Now, we just need to multiply these two results together to get the final answer. So, we have 28 multiplied by 72. Let's do the math: 28 * 72 = 2016. Therefore, the solution to the entire expression (4²•2-⁴) • (5²•3-³) is 2016. Congratulations, we've cracked it! See how all the steps we took, from understanding the order of operations to solving each part individually, culminated in this final answer? It’s like climbing a mountain; each step takes effort, but the view from the top is worth it. This final calculation is the culmination of all our hard work and demonstrates the power of methodical problem-solving. We started with a seemingly complex expression and, through careful analysis and step-by-step execution, arrived at a clear and definitive solution. This is the essence of mathematics: turning complexity into clarity.

The Beauty of Math: Step-by-Step Solutions

Wow, what a journey! We've successfully unraveled the expression (4²•2-⁴) • (5²•3-³), arriving at the answer 2016. But more than just getting the answer, we've explored the process, understanding the order of operations and how to break down complex problems into manageable steps. This is the real beauty of mathematics – it's not just about the solution, but about the logical thinking and problem-solving skills we develop along the way. Each problem is a new challenge, an opportunity to sharpen our minds and expand our understanding. And remember, even the most daunting problems can be conquered if we approach them methodically and break them down into smaller, more digestible parts. So, the next time you encounter a complex mathematical expression, don't shy away from it. Embrace the challenge, take it step by step, and enjoy the journey of discovery! Mathematics is a language, a tool, and a way of thinking that empowers us to understand the world around us. Keep exploring, keep learning, and keep enjoying the beauty of math!