Step-by-Step Guide Solving 3^2 * 9^2 / 27

Hey guys! Today, we're diving into a fun math problem: solving 3^2 times 9^2 divided by 27. Don't worry, it might look intimidating at first, but we'll break it down step by step so you can conquer it with ease. Whether you're brushing up on your math skills or tackling homework, this guide will make the process super clear. So, grab your pencils, and let's get started!

Understanding the Basics

Before we jump into the problem, let’s quickly recap the basics of exponents and the order of operations. Exponents, like the little 2 in 3^2, tell you how many times to multiply a number by itself. So, 3^2 means 3 multiplied by 3. Got it? Great! Now, the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), tells us the sequence in which we should perform mathematical operations. This is super important because doing things in the wrong order can totally mess up your answer. In our problem, we have exponents, multiplication, and division. According to PEMDAS, we'll tackle the exponents first, then move from left to right through multiplication and division. Remember, division and multiplication hold the same priority, so we perform them in the order they appear from left to right. This might sound like a mouthful, but trust me, it’ll become second nature as we work through the problem. Understanding these foundational concepts is key to cracking this and many other math problems. Think of it like building a house; you need a solid foundation before you can start putting up the walls. So, with our basics in place, let’s move on to simplifying the expression!

Step 1: Simplify the Exponents

Okay, let’s kick things off by simplifying the exponents in our expression: 3^2 times 9^2 divided by 27. Remember, an exponent tells us how many times to multiply the base number by itself. So, 3^2 means 3 multiplied by 3, and 9^2 means 9 multiplied by 9. Let's calculate these: 3^2 = 3 * 3 = 9. Easy peasy, right? Now let's tackle 9^2: 9^2 = 9 * 9 = 81. Awesome! We've simplified our exponents, and now our expression looks a bit more manageable. Instead of dealing with exponents, we now have simple numbers. Our problem has transformed from 3^2 * 9^2 / 27 into 9 * 81 / 27. See how breaking down the problem into smaller steps makes it less daunting? This is a fantastic strategy for tackling any mathematical challenge. By simplifying the exponents first, we've cleared the path for the next operations. Now, we're ready to move on to the multiplication and division, keeping in mind our trusty PEMDAS guide. Remember, we handle these operations from left to right, which is crucial for getting the correct answer. So, with our exponents tamed, let's dive into the next step and keep this math train rolling!

Step 2: Perform Multiplication

Now that we've simplified the exponents, let's move on to the multiplication part of our problem. Our expression currently looks like this: 9 * 81 / 27. According to the order of operations (PEMDAS), we handle multiplication and division from left to right. So, the first operation we need to tackle is 9 multiplied by 81. Let’s get to it! 9 * 81 equals 729. Great job! We've successfully performed the multiplication. Our expression has now been simplified further, and it looks like this: 729 / 27. See how we're chipping away at the problem piece by piece? This is the beauty of a step-by-step approach. By focusing on one operation at a time, we avoid confusion and reduce the chance of making mistakes. This is especially helpful when dealing with more complex equations. Now that we've handled the multiplication, we're left with a simple division problem. We're in the home stretch, guys! All that's left is to divide 729 by 27. So, let’s jump into the final step and bring this problem to a triumphant conclusion. Are you ready to see the final answer? Let’s go!

Step 3: Perform Division

Alright, we've reached the final step in solving our problem: 3^2 times 9^2 divided by 27. We've already simplified the exponents and performed the multiplication, and now we're staring at the division. Our expression currently reads 729 / 27. This is the last hurdle, and we're going to nail it! So, let's divide 729 by 27. If you do the math, you'll find that 729 divided by 27 equals 27. Woo-hoo! We did it! We've successfully performed all the necessary operations, and we've arrived at our final answer. Isn't it satisfying to solve a problem like this from start to finish? By breaking it down into manageable steps, we transformed a seemingly complex expression into a straightforward calculation. This is a valuable skill in mathematics and in life in general. When faced with a challenge, breaking it into smaller, actionable steps can make it much less intimidating. Now that we've completed the division, we have our final answer. So, let's take a moment to summarize our journey and celebrate our achievement!

Final Answer and Summary

So, after all our hard work, what's the final answer to 3^2 times 9^2 divided by 27? Drumroll, please… The answer is 27! Fantastic job, guys! We took a problem that looked a bit complicated at first glance and broke it down into simple, manageable steps. First, we simplified the exponents: 3^2 became 9, and 9^2 became 81. Then, we performed the multiplication: 9 times 81 equals 729. Finally, we tackled the division: 729 divided by 27 gives us our answer of 27. Throughout this process, we stuck to the order of operations (PEMDAS), which ensured we solved the problem correctly. Remember, the order of operations is your best friend in mathematics. It’s like a roadmap that guides you through the steps you need to take. We also learned the importance of breaking down complex problems into smaller steps. This is a strategy you can use not just in math but in many areas of life. By focusing on one step at a time, you can make any challenge seem less daunting. So, congratulations on solving this problem with me! I hope this step-by-step guide has been helpful and has boosted your confidence in tackling similar math problems. Keep practicing, and you'll become a math whiz in no time!