Math Problem: Solving (+2)⁴ - (-50) : (-10) Explained
Hey guys! Let's dive into this math problem: (+2)⁴ - (-50) : (-10). Don't worry, it looks a bit intimidating at first glance, but we'll break it down step-by-step. This problem involves several mathematical operations, including exponentiation, subtraction, and division. Understanding the order of operations (PEMDAS/BODMAS) is key to solving this correctly. We'll go through each part meticulously, making sure we don't miss anything. The goal is to arrive at the correct answer while understanding why each step is taken. It's not just about getting the right number; it's also about learning the process. Ready to get started? Let's go!
Understanding the Order of Operations (PEMDAS/BODMAS)
Before we jump into the calculation, it's crucial to understand the order of operations. You might know it as PEMDAS or BODMAS. These acronyms help us remember the sequence in which we solve mathematical expressions. PEMDAS stands for: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS is similar, representing: Brackets, Orders (powers/indices), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). Both are the same, just with different names! In our problem, we've got exponents, subtraction, and division, so we'll follow PEMDAS/BODMAS to make sure we get the right answer. First, we deal with anything inside the parentheses or brackets. Then we will address the exponents (powers). After that, we handle multiplication and division (working from left to right). Finally, we'll take care of addition and subtraction (also from left to right). Following this order is super important because it guarantees that everyone arrives at the same solution. If you're wondering why this order is used, it's because it's a convention that ensures consistency in mathematical calculations, which is critical for all areas of math, science, and even daily life!
Let's apply this to our problem (+2)⁴ - (-50) : (-10). We don’t have parentheses in the traditional sense, but we do have exponents. So we'll deal with those first.
Step-by-step breakdown
Let's meticulously solve the mathematical problem (+2)⁴ - (-50) : (-10) by following the order of operations (PEMDAS/BODMAS). This detailed, step-by-step explanation ensures clarity and understanding. Initially, we will perform exponentiation. Then, we will address division, and finally, subtraction to reach the definitive solution. The goal is to clarify each step, providing a comprehensive approach for everyone involved. This method facilitates learning, allowing you to replicate and understand mathematical operations with greater ease. This approach is really helpful for anyone looking to brush up on their math skills or to understand the mechanics behind the problem. It is designed to make math accessible and understandable. Remember, the key is to perform each operation in the correct sequence to prevent errors and ensure that you get the right answer.
Breaking Down (+2)⁴
Alright, let's start with the first part of our expression: (+2)⁴. This means we need to raise positive two to the power of four. An exponent (the small number, 4 in this case) tells us how many times to multiply the base number (the number being raised to the power, which is 2 in our case) by itself. So (+2)⁴ is the same as 2 * 2 * 2 * 2. It’s like saying, “multiply 2 by itself, four times.” This step results in 16. Remember, we don't have to worry about the plus sign inside the parentheses here; it just indicates a positive number. Calculating exponents like this is a fundamental skill in mathematics and essential for more complex equations. Understanding how exponents work forms the base for understanding higher-level math. So, after calculating (+2)⁴ we obtain 16. It's a straight forward application of the exponent, and we've successfully addressed the first part of our problem. This step simplifies our expression and gets us closer to the final answer. Remember, always double-check your calculations to avoid mistakes!
Now, let's move on to the next part of the equation.
Calculation process
So, after calculating (+2)⁴ and finding that it equals 16, we move to the next part of the expression: (-50) : (-10). The colon (:) represents division. Here, we're dividing -50 by -10. When you divide a negative number by another negative number, the result is always positive. This is a crucial rule to remember in mathematics. So, -50 divided by -10 equals 5. The negative signs cancel each other out during the division. Understanding the rules for handling negative numbers is essential to prevent mistakes. Many people find dealing with negative numbers to be a bit tricky, but with practice, it becomes easy. This step involves a simple division, but the sign rule is essential. Keeping track of signs is vital in all calculations. We've now successfully completed the division part of our problem, and we are close to our final answer. It may seem simple, but precision at this stage is very important. Getting the sign wrong can completely change the answer!
Solving the Subtraction
Okay, now that we've dealt with the exponent and the division, we're left with the subtraction part of the problem. Remember, our original equation was (+2)⁴ - (-50) : (-10). We've simplified this to 16 - 5 (because (+2)⁴ equals 16 and (-50) : (-10) equals 5). Now, we just need to subtract 5 from 16. It's a straightforward subtraction problem: 16 - 5 = 11. That's it! We've solved the entire equation. This step is the final calculation required to get the answer. This is where you put all the previous steps together, simplifying the equation even more. This subtraction, although simple, is essential to reach the correct solution. It underscores how the order of operations and the correct execution of each step lead to the right answer. Congratulations! Now you can solve equations like this with confidence! Now, we have successfully completed all the steps and arrived at the solution. Keep practicing to reinforce your understanding and sharpen your skills.
Bringing it all together
By following the order of operations, we've broken down a seemingly complex math problem into manageable steps. Remember the PEMDAS/BODMAS? First, we handled the exponent in (+2)⁴ and got 16. Then, we did the division (-50) : (-10), which resulted in 5. Finally, we performed the subtraction: 16 - 5, arriving at the final answer of 11. This process not only solves the problem but also reinforces the importance of each mathematical rule. Math is all about taking complex things and simplifying them. With each step, it's getting easier. Solving this math problem correctly requires a solid grasp of exponents, division rules (especially concerning negative numbers), and basic subtraction. The crucial thing is to remember the order in which these operations are done. The consistent application of the order of operations (PEMDAS/BODMAS) is the key to solving this and other math problems. The result highlights the importance of precise calculation in math. Always recheck your answers to catch any potential errors and confirm your knowledge.
The Final Answer
So, after all that work, the answer to (+2)⁴ - (-50) : (-10) is 11. Great job, guys! You've successfully solved this mathematical problem. By following the order of operations, step-by-step, we've reached the correct solution. Remember, math is like a puzzle; each step brings you closer to solving it. With a little practice, problems like these become easier and easier. Keep practicing, and you will become proficient at solving math problems. The goal is not just to find the correct answer, but also to understand how to find it. Keep in mind that math can be fun and rewarding, and with the right approach, anyone can master it. Congrats! You've learned how to solve this math problem. Always keep practicing, and remember the rules, and you'll be acing math problems in no time! Keep practicing and you will do great!