Solving The Math Problem: A Step-by-Step Guide
Hey guys! Let's break down this math problem: 4² + 5² + 6² + 2 * (4² - 2³ - 8) + 25 - 16 : 50; [5 - (5² + 321 : 320) + (3²)² + (285 - 81) : 10²]. It looks a bit intimidating at first glance, but trust me, we can tackle it step by step. We'll use the order of operations (PEMDAS/BODMAS) to make sure we get the right answer. This will ensure that we don't miss anything and that we understand the process completely. The problem has a lot of different operations, including exponents, multiplication, subtraction, addition, and division. The key to solving this problem is to go slow and be organized. We'll first look at the exponents, then the parentheses and brackets, then the multiplication and division, and finally, the addition and subtraction. If we follow this order, we should be able to get the correct answer. I know it seems like a lot, but just stick with me, and we'll get through it together. By the end of this, you'll be able to solve similar problems with confidence. Let's dive in and have some fun!
Step-by-Step Solution
Alright, let's roll up our sleeves and get to work. We'll go through each part of the equation methodically, starting with the exponents. This is where we take care of those little numbers up top. Then, we will go through the Parentheses and Brackets, remember that the order is important! We'll then focus on multiplication and division from left to right. Next, we will move to addition and subtraction from left to right. Don't worry, I'll guide you every step of the way. Let's keep the momentum going. Keep in mind that understanding each step is more important than just getting the answer. Let's begin!
Exponents First
First things first, let's tackle those exponents. Remember, an exponent tells us how many times to multiply a number by itself. We have several exponents in this problem: 4², 5², 6², 2³, and 3². Let's calculate those:
- 4² = 4 * 4 = 16
- 5² = 5 * 5 = 25
- 6² = 6 * 6 = 36
- 2³ = 2 * 2 * 2 = 8
- 3² = 3 * 3 = 9
Now, let's substitute these values back into the original equation. The equation now looks like this: 16 + 25 + 36 + 2 * (16 - 8 - 8) + 25 - 16 : 50; [5 - (25 + 321 : 320) + 9² + (285 - 81) : 10²]. Getting those exponents sorted out makes the rest of the problem a lot easier to handle. We've simplified the equation, and we're well on our way. High five for getting through the first step!
Parentheses and Brackets
Next up, we will resolve the expressions inside the parentheses and brackets. Remember to work from the innermost parentheses outwards. Within the first set of parentheses, we have (16 - 8 - 8). Let's calculate that: 16 - 8 - 8 = 0. Now, we will address the contents within the brackets which are [5 - (25 + 321 : 320) + 9² + (285 - 81) : 10²]. Let's start with the inner part (25 + 321 : 320), let's handle the division first: 321 : 320 = 1.003125. So now we have (25 + 1.003125) = 26.003125. After that we need to solve 9² and 10² which we know are 81 and 100, respectively. Now let's solve the brackets: [5 - 26.003125 + 81 + (285-81) : 100], which is [5 - 26.003125 + 81 + 204 : 100]. Lastly, we divide 204 : 100 = 2.04. Let's make the last calculation: [5 - 26.003125 + 81 + 2.04] which is [61.036875].
Let's substitute these values back into the equation, we now have: 16 + 25 + 36 + 2 * (0) + 25 - 16 : 50; [61.036875]. Isn't this getting more manageable? We're simplifying things and making the problem easier to solve. Keep up the good work!
Multiplication and Division
Time to handle multiplication and division. Remember to work from left to right. In our equation, we have two multiplications: 2 * (0) and - 16 : 50; [61.036875]. Let's calculate those:
- 2 * (0) = 0
- 16 : 50 = 0.32
Now, our equation is: 16 + 25 + 36 + 0 + 25 - 0.32; [61.036875]. We're getting closer to the finish line. Only a few more steps to go. You're doing great!
Addition and Subtraction
Finally, we're down to addition and subtraction. We work from left to right. Let's calculate it: 16 + 25 + 36 + 0 + 25 - 0.32. This will be 101 - 0.32 = 100.68. And we finally get the answer to [61.036875]. Thus, we finally get 100.68 ; [61.036875]. This problem is a bit complex because it involves multiple steps and different mathematical operations, but we've successfully navigated through each of them. And there you have it, the final answer! You've made it through the whole equation! Give yourself a pat on the back. You've shown that with careful step-by-step work, even complex problems can be solved!
Conclusion
Congrats, guys! You've successfully solved the math problem! We've covered exponents, parentheses, multiplication, division, addition, and subtraction. You've now seen how to break down a complex mathematical expression into manageable steps. Keep practicing, and you'll get even more confident. Keep in mind that consistency is key. Do not be discouraged by complex problems. Each problem you solve will make you stronger and better at math. Great job! Now, go forth and conquer those equations! And remember, it's all about understanding the steps and keeping a positive attitude.
