Solving (9+3)²x(5-2)⁴÷(8+2²): A Step-by-Step Guide

by Tom Lembong 51 views
Iklan Headers

Alright, guys, let's break down this mathematical expression step by step. We're going to solve: (9+3)²x(5-2)⁴÷(8+2²). Don't worry, it's not as intimidating as it looks! We'll go through each part, making sure everything is crystal clear. So, grab your calculators or a piece of paper, and let's get started!

Understanding the Order of Operations

Before we dive in, it's super important to remember the order of operations, often remembered by the acronym PEMDAS, which stands for:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

This order tells us exactly what to tackle first to ensure we get the correct answer. So, keep PEMDAS in mind as we go through each step.

First things first: Parentheses

Okay, the first thing we need to do is deal with what's inside the parentheses. We've got two sets of parentheses in our expression:

  1. (9 + 3)
  2. (5 - 2)
  3. (8 + 2²)

Let's simplify each one:

  • 9 + 3 = 12
  • 5 - 2 = 3
  • 8 + 2² = 8 + 4 = 12

So, our expression now looks like this: 12² x 3⁴ ÷ 12

Next up: Exponents

Now that we've handled the parentheses, we move on to the exponents. We have two exponents to take care of:

  1. 12² (which means 12 * 12)
  2. 3⁴ (which means 3 * 3 * 3 * 3)

Let's calculate those:

  • 12² = 144
  • 3⁴ = 81

Our expression is now: 144 x 81 ÷ 12. See? We're making progress!

Multiplication and Division

Alright, the next step is multiplication and division. Remember, we do these from left to right. So, first, we multiply:

  • 144 x 81 = 11664

Now, our expression is: 11664 ÷ 12. Finally, we divide:

  • 11664 ÷ 12 = 972

So, the final answer is 972. Woo-hoo! We did it!

Breaking Down Each Step with Examples

To really solidify our understanding, let's dive deeper into each step with some extra examples. This will help you tackle similar problems with confidence.

Parentheses: Examples

Parentheses are like little containers that tell you, "Hey, do this first!" Here are a couple more examples:

  • (4 + 2) x 3
    • First, 4 + 2 = 6
    • Then, 6 x 3 = 18
  • 10 - (2 x 3)
    • First, 2 x 3 = 6
    • Then, 10 - 6 = 4

Exponents: Examples

Exponents tell you how many times to multiply a number by itself. Let's look at a few more examples:

  • 5³ (5 cubed) = 5 * 5 * 5 = 125
  • 2⁵ (2 to the power of 5) = 2 * 2 * 2 * 2 * 2 = 32

Multiplication and Division: Examples

Multiplication and division are pretty straightforward, but remember to work from left to right if they're both in the same expression:

  • 6 x 4 ÷ 2
    • First, 6 x 4 = 24
    • Then, 24 ÷ 2 = 12
  • 15 ÷ 3 x 4
    • First, 15 ÷ 3 = 5
    • Then, 5 x 4 = 20

Why Order of Operations Matters

You might be wondering, "Why do we even need this order of operations thing?" Well, if we didn't follow the same rules, we could end up with totally different answers! Let's illustrate this with an example.

Consider the expression: 5 + 2 x 3

  • Correct way (following PEMDAS):
    • First, 2 x 3 = 6
    • Then, 5 + 6 = 11
  • Incorrect way (adding first):
    • First, 5 + 2 = 7
    • Then, 7 x 3 = 21

See the difference? By not following PEMDAS, we got a completely different result. That's why it's so crucial to stick to the order of operations.

Common Mistakes to Avoid

Even with a good understanding of PEMDAS, it's easy to slip up. Here are some common mistakes to watch out for:

  • Forgetting to work from left to right: When you have multiplication and division (or addition and subtraction) in the same expression, always work from left to right.
  • Ignoring parentheses: Parentheses are your best friends! Always tackle what's inside them first.
  • Misunderstanding exponents: Make sure you're multiplying the base number by itself the correct number of times.

Practice Problems

Okay, let's put your skills to the test! Here are a few practice problems for you to try:

  1. (6 + 4)² ÷ 5
  2. 10 - 2 x 3 + 1
  3. 4³ - (8 ÷ 2) x 5

Work through these problems, keeping PEMDAS in mind. Check your answers with a calculator or ask a friend to double-check.

Real-World Applications

You might be thinking, "When am I ever going to use this in real life?" Well, math is everywhere! Here are a few examples of how the order of operations comes in handy:

  • Calculating expenses: If you're figuring out your monthly budget, you need to add up all your expenses in the correct order.
  • Cooking: When you're scaling a recipe up or down, you need to make sure you're multiplying and dividing ingredients correctly.
  • Programming: In computer programming, the order of operations is crucial for writing code that performs calculations correctly.

Tips and Tricks for Success

Here are some extra tips to help you master the order of operations:

  • Write it out: When you're solving a problem, write out each step clearly. This will help you keep track of what you're doing and avoid mistakes.
  • Use parentheses: If you're not sure about the order of operations, use parentheses to make it clear what you want to do first.
  • Practice regularly: The more you practice, the better you'll become at applying the order of operations.

Conclusion

So, there you have it! We've tackled the expression (9+3)²x(5-2)⁴÷(8+2²) and broken down the order of operations step by step. Remember PEMDAS, avoid common mistakes, and practice regularly, and you'll be a math whiz in no time! Keep practicing, and you'll find these types of problems become second nature.

If you have any questions or need more help, don't hesitate to ask. Happy calculating!