Math Problem Solutions A, B, C

Hey guys! Math can be super fun once you get the hang of it. Let's break down these problems step by step so we can understand exactly what's going on. We've got some exponents and multiplications to tackle, so let's jump right in and make sure we're crystal clear on every step.

Understanding the Basics

Before we dive into the specific problems, it’s essential to make sure we’re on the same page with the foundational concepts. Math isn't just about crunching numbers; it’s about understanding the rules that govern those numbers. Exponents, for instance, tell us how many times to multiply a number by itself. When we see something like (-7)², it means we’re multiplying -7 by -7. Simple enough, right? But what happens when we throw in more complex operations? That's where the order of operations comes into play. Remember PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order ensures we all get the same answer, no matter who's solving the problem. Without it, math would be chaotic! Now, let's talk about negative numbers. Multiplying two negative numbers gives us a positive result, while multiplying a negative and a positive number yields a negative result. This is super important when dealing with expressions like (-7)², where a negative number is squared, turning it positive. And then there are the properties of exponents. When multiplying numbers with the same base, we add their exponents. So, (-7)² multiplied by (-7)³ becomes (-7) raised to the power of 2+3, which is 5. These rules might seem like little details, but they're the bedrock of mathematical problem-solving. Mastering them is like having the secret decoder ring for any math puzzle. So, as we tackle the specific problems below, keep these basics in mind. They'll be our guide, our trusty tools, as we navigate the world of exponents and calculations. And remember, there's no such thing as a silly question. If something doesn’t quite click, ask away! We’re in this together, and the goal is to make math make sense, for everyone.

Problem A: (-7)². (-7)³ - 7

Okay, let's tackle the first one. We've got (-7)² multiplied by (-7)³, and then we subtract 7. Remember our order of operations? Exponents first! So, let's break it down:

First, we handle the exponents. (-7)² means -7 multiplied by -7, which equals 49. A negative times a negative is a positive! Next, we have (-7)³. This is -7 times -7 times -7. As we just figured out, the first two -7s give us 49, and then we multiply by -7 again. 49 times -7 is -343. So, (-7)³ is -343. Now we've simplified our expression to 49 multiplied by -343, minus 7. See how breaking it down makes it less scary?

Now, let's move on to the multiplication. We're multiplying 49 by -343. This is a bit of a bigger calculation, but no problem! 49 times -343 equals -16807. We've got a large negative number, but we're not done yet. Our expression is now -16807 minus 7. Time for the final step: subtraction. We're subtracting 7 from -16807. When you subtract from a negative number, you're moving further into the negatives. Think of it like temperature: if it's already -16807 degrees and it drops another 7 degrees, it gets even colder. So, -16807 minus 7 equals -16814. And that's our final answer! See, we took a seemingly complex problem and, by breaking it down into smaller steps and remembering our rules, we cracked it. Math is like a puzzle, and each piece fits perfectly when we follow the instructions. Keep this approach in mind as we move on to the next problem. It’s all about methodically working through each operation, one at a time. And if you ever feel stuck, remember: go back to the basics, double-check your steps, and don’t be afraid to ask for help. We’re learning this together!

Problem B: 3⁵ . g ⁴ . 2 / 3⁵ - (3²)²

Alright, let's dive into problem B! This one looks a bit more complex with fractions and exponents all mixed together, but don't worry, we'll tackle it step by step, just like before. Remember PEMDAS/BODMAS? It's our best friend here. First up: exponents. We've got 3⁵, which means 3 multiplied by itself five times. Let's calculate that: 3 * 3 * 3 * 3 * 3. That's 9 * 9 * 3, which is 81 * 3, and that equals 243. So, 3⁵ is 243. Now, we also have g⁴. Hmmm, this is interesting because 'g' isn't a number. It's a variable! This means we can't actually calculate a numerical value for g⁴ unless we know what 'g' stands for. For now, we'll just leave it as g⁴. Next in the exponent line-up is (3²)². This means we first calculate 3², which is 3 * 3 = 9. Then, we square that result, so we have 9², which is 9 * 9 = 81. So, (3²)² equals 81. We've powered through the exponents! Our expression is now 243 . g⁴ . 2 / 243 - 81. See how much simpler it's becoming? Now, let's handle the multiplication and division. We have 243 multiplied by g⁴, multiplied by 2, all divided by 243. Multiplication and division are done from left to right, so let's start there. We can rewrite this part as (243 * g⁴ * 2) / 243. Notice something cool? We're multiplying by 243 and then dividing by 243. These operations essentially cancel each other out! It's like multiplying by 2 and then dividing by 2 – you end up back where you started. So, the 243s cancel out, leaving us with just g⁴ multiplied by 2, or 2g⁴. We're almost there! Our expression is now 2g⁴ - 81. Finally, we have subtraction. We're subtracting 81 from 2g⁴. But remember, 'g' is a variable. We can't combine terms that are different, like terms with 'g' and constant numbers. So, we've simplified this expression as much as we can. Our final, simplified expression is 2g⁴ - 81. Unless we know the value of 'g', this is as far as we can go. This problem was a great example of how to use PEMDAS/BODMAS to break down complex expressions. We tackled exponents, multiplication, division, and even a variable! Remember, the key is to take it one step at a time and follow the rules. You got this!

Problem C: 2 . 16 + 4 = ?

Let's jump into our final problem, problem C! This one looks a bit shorter and simpler than the others, but we still need to be careful to follow the order of operations. We have 2 multiplied by 16, plus 4. What's the first thing we need to do? You guessed it – multiplication comes before addition in PEMDAS/BODMAS! So, we start by multiplying 2 and 16. What's 2 times 16? It's 32! Now we've simplified our expression to 32 + 4. We're almost home! All that's left is the addition. We need to add 4 to 32. What's 32 plus 4? It's 36! So, the answer to our problem is 36. We did it! Problem C is solved. See how following the order of operations makes the problem straightforward? If we had added 16 and 4 first, we would have gotten a completely different (and incorrect) answer. This highlights why PEMDAS/BODMAS is so crucial in math. It ensures we all arrive at the same correct solution, no matter how we approach the problem. Now that we've tackled all three problems, take a moment to appreciate what we've accomplished. We've worked with exponents, negative numbers, variables, multiplication, division, addition, and subtraction. We've used the order of operations to guide us, and we've broken down complex problems into manageable steps. Math can sometimes feel like climbing a mountain, but each step we take brings us closer to the summit. And every time we solve a problem, we strengthen our mathematical muscles. So, give yourself a pat on the back for your hard work and dedication. You're doing great!

Original Question: Hitung: a. (-7)². (-7)3 -7 b. 35. g 4. 2 " 35 - (32) 2 " " C. 2. 16+4 =? Discussion category: matematika

Repaired and Clarified Questions:

Here are the repaired and clarified versions of the math problems, making them easier to understand and solve:

• a. Calculate (-7)² * (-7)³ - 7
• b. Simplify 3⁵ * g⁴ * 2 / 3⁵ - (3²)²
• c. Evaluate 2 * 16 + 4

Math Problem Solutions A, B, and C are provided to improve understanding and problem-solving skills. Math is fun and engaging when broken down step by step!