Simplify $6^2 \cdot(4-2)+2^3+6^2$: Step-by-Step Guide

Aug 8, 2025 by Felix Dubois 54 views

$Simplify: $6^2 \cdot(4-2)+2^3+6^2$$

Hey guys! Let's break down this math problem together, making sure everything is crystal clear and super easy to follow. We're tackling the expression $6^2 \cdot(4-2)+2^3+6^2$ , and we'll use the order of operations (PEMDAS/BODMAS) to solve it. Trust me, by the end of this, you'll be a pro at simplifying expressions like this!

Understanding the Order of Operations

Before we dive into the nitty-gritty, let's quickly recap the order of operations. Remember PEMDAS/BODMAS? It stands for:

Parentheses / Brackets
Exponents / Orders
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

This is the golden rule in simplifying mathematical expressions, ensuring we all arrive at the same correct answer. So, keep this in mind as we move forward, guys! We'll be using it every step of the way.

Step-by-Step Simplification

Okay, let's get our hands dirty with the problem: $6^2 \cdot(4-2)+2^3+6^2$ . We'll go through it step-by-step, making sure we don’t miss anything. Ready? Let’s do this!

1. Parentheses/Brackets

The first thing we spot is the parentheses: $(4-2)$ . This is our starting point. Inside the parentheses, we have a simple subtraction. Let's take care of that:

$4 - 2 = 2$

So, our expression now looks like this:

$6^2 \cdot 2 + 2^3 + 6^2$

See? We're already making progress. One step down, and several more to go. Keep it up, guys!

2. Exponents/Orders

Next up are the exponents. We have two terms with exponents: $6^2$ and $2^3$ . Let's simplify each of them.

$6^2$ means 6 multiplied by itself: $6 \cdot 6 = 36$
$2^3$ means 2 multiplied by itself three times: $2 \cdot 2 \cdot 2 = 8$

Now, let's replace these values in our expression:

$36 \cdot 2 + 8 + 36$

Looking good, right? We've tackled the exponents, and things are getting simpler and simpler. We're on a roll, guys!

3. Multiplication

Now we move onto multiplication and division. In our expression, we only have multiplication: $36 \cdot 2$ . Let's do the math:

$36 \cdot 2 = 72$

Replace this back into our expression:

$72 + 8 + 36$

Awesome! We've knocked out the multiplication. Now, we're left with just addition. This is the home stretch, guys!

4. Addition

Finally, we have addition. We just need to add the numbers together from left to right:

$72 + 8 + 36$

First, add $72$ and $8$ :

$72 + 8 = 80$

Now, add the result to $36$ :

$80 + 36 = 116$

And there we have it! We've simplified the entire expression.

The Final Answer

So, the simplified form of $6^2 \cdot(4-2)+2^3+6^2$ is:

$116$

Woohoo! We did it! You've successfully simplified this mathematical expression by following the order of operations. Give yourselves a pat on the back, guys! You're becoming math whizzes!

Breaking Down the Solution

Let's recap what we did, just to make sure everything is crystal clear. We started with the original expression:

$6^2 \cdot(4-2)+2^3+6^2$

Then, we followed these steps:

Parentheses: $4 - 2 = 2$
Exponents: $6^2 = 36$ and $2^3 = 8$
Multiplication: $36 \cdot 2 = 72$
Addition: $72 + 8 + 36 = 116$

Each step was crucial, and by sticking to the order of operations, we arrived at the correct answer. Remember, guys, math is like building with LEGOs – each step builds upon the previous one. If you follow the instructions, you'll create something amazing!

Why is Order of Operations Important?

You might be wondering, “Why do we even need this order of operations thing?” Well, imagine if we didn't have a set order. Different people could interpret the same expression in different ways, leading to different answers. Chaos, right?

The order of operations ensures that everyone solves the problem in the same way, leading to a consistent and correct answer. It's like a universal language for math. So, next time you're simplifying an expression, remember PEMDAS/BODMAS – it's your best friend in the math world, guys!

Practice Makes Perfect

Now that we've simplified this expression together, the best way to really master this skill is to practice. Try simplifying other expressions using the order of operations. You can find plenty of examples online or in your math textbook. The more you practice, the more comfortable and confident you'll become.

Remember, math isn't about memorizing formulas; it's about understanding the process and applying it. So, keep practicing, keep exploring, and keep having fun with it, guys! You've got this!

Conclusion

Simplifying expressions might seem daunting at first, but with a clear understanding of the order of operations and a bit of practice, it becomes a piece of cake. We tackled the expression $6^2 \cdot(4-2)+2^3+6^2$ step-by-step, and we successfully simplified it to $116$ .

So, the next time you encounter a similar problem, remember our journey together. Remember PEMDAS/BODMAS, break the problem down into smaller steps, and take it one step at a time. You'll be simplifying expressions like a pro in no time, guys!

Keep up the great work, and never stop learning. You're all amazing, and I'm super proud of you for diving into this math problem with me. Until next time, happy simplifying!