Solve: [8²-(9x2-10)]+2² Step-by-Step Guide

by Benjamin Cohen 43 views

Hey guys! Ever find yourself staring at a math problem that looks like it belongs in another galaxy? Don't worry, we've all been there. Today, we're going to break down a seemingly complex equation into bite-sized pieces. We'll tackle the problem [8²-(9x2-10)]+2² step-by-step, so you can not only solve it but also understand why we're doing each operation. Math can be super fun once you get the hang of it, so let's dive in!

Understanding the Order of Operations

Before we even think about touching the equation itself, we need to chat about the golden rule of math: the order of operations. Think of it as the traffic laws of the mathematical world. If you don't follow them, you're gonna have a bad time (or at least, a wrong answer!). The most common way to remember this order is through the acronym PEMDAS, which stands for:

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

Basically, this tells us that we need to deal with parentheses first, then exponents, then multiplication and division (working from left to right), and finally, addition and subtraction (again, from left to right). Keep PEMDAS in the back of your mind as we work through the problem. It's our trusty map for this mathematical adventure. Neglecting the order of operations can lead to drastically incorrect answers, making it crucial to adhere to PEMDAS. For instance, solving this expression from left to right without considering PEMDAS would involve subtracting before addressing the parentheses and exponents, thus leading to a wrong answer. Therefore, a clear understanding of the order of operations is paramount to solving mathematical expressions accurately. This principle ensures consistency and accuracy in mathematical calculations across different contexts and applications. Now that we've refreshed our understanding of PEMDAS, we're well-equipped to tackle the problem at hand and dissect it piece by piece, ensuring we arrive at the correct solution. This foundational knowledge will not only help us solve this specific equation but will also prove invaluable for tackling more complex mathematical problems in the future.

Step 1: Tackling the Parentheses

Okay, so the first thing we see in our equation [8²-(9x2-10)]+2² are those parentheses. PEMDAS tells us these are our first priority. Inside the parentheses, we have (9x2-10). Now, within the parentheses, we need to follow PEMDAS again! So, what comes first: multiplication or subtraction? Multiplication, of course!

So, let's do 9 x 2, which equals 18. Now our expression inside the parentheses looks like this: (18 - 10). Easy peasy! Now we just subtract 10 from 18, which gives us 8. So, we've successfully simplified the expression inside the parentheses to 8. This is a huge step! We've taken a chunk of the equation and made it much simpler. Remember, breaking down complex problems into smaller, manageable steps is key to success in math (and in life, really!). The beauty of following PEMDAS is that it provides a structured approach to problem-solving, ensuring that we tackle each part of the equation in the correct order. This not only leads to the correct answer but also minimizes the chances of making errors along the way. As we continue to solve the equation, you'll see how each step builds upon the previous one, highlighting the importance of a solid foundation in the order of operations. By focusing on the parentheses first, we've effectively isolated a portion of the equation, making it less daunting and more approachable. This strategy of simplification is a powerful tool in mathematics, allowing us to conquer even the most intimidating-looking problems with confidence.

Step 2: Evaluating the Exponents

Now that we've conquered the parentheses, let's move on to the next item on our PEMDAS checklist: exponents. Looking back at our equation, which now looks like [8²-8]+2², we see two exponents: 8² and 2². Remember, an exponent tells us how many times to multiply a number by itself. So, 8² means 8 multiplied by itself (8 x 8), and 2² means 2 multiplied by itself (2 x 2).

Let's start with 8². 8 x 8 equals 64. Great! Now let's tackle 2². 2 x 2 equals 4. Awesome! We've now simplified our exponents, and our equation is starting to look even cleaner. It now reads: [64-8]+4. See how much progress we're making? By systematically addressing each part of the equation according to PEMDAS, we're gradually unraveling the complexity and bringing the solution within reach. Exponents often seem intimidating at first glance, but they're really just a shorthand way of expressing repeated multiplication. Understanding this fundamental concept makes them much less scary and a whole lot easier to work with. As we continue through the steps, you'll notice how simplifying exponents early on helps to streamline the rest of the calculation process. This methodical approach is what makes PEMDAS such a valuable tool for solving mathematical expressions efficiently and accurately. So, with the exponents tamed, we're one step closer to our final answer. Let's keep the momentum going and see what awaits us in the next step!

Step 3: Addressing the Remaining Parentheses (Brackets)

You might be thinking,