Powers Calculation: Step-by-Step Math Problems Solved
Hey guys! Today, we're diving into some cool math problems involving powers. We're going to break down each problem step by step, so you can easily understand how to solve them. Whether you're a student tackling homework or just brushing up on your math skills, this guide is for you. So, let's get started and make math fun!
a) 7 * 7 + 3 * 3 - 3
In this first problem, we need to use powers to rewrite the expression and then calculate the result. It's all about understanding how to express numbers as powers and then applying the order of operations. This is a fundamental concept in mathematics, and mastering it will help you tackle more complex problems later on. So, let's break it down together and see how we can solve this! First, let's rewrite the expression using powers:
- 7 * 7 can be written as 72 (7 squared)
- 3 * 3 can be written as 32 (3 squared)
So, the expression becomes: 72 + 32 - 3.
Now, let's calculate the powers:
- 72 = 7 * 7 = 49
- 32 = 3 * 3 = 9
Substitute these values back into the expression:
49 + 9 - 3
Now, perform the addition and subtraction from left to right:
- 49 + 9 = 58
- 58 - 3 = 55
Therefore, 7 * 7 + 3 * 3 - 3 = 55.
Guys, it's super important to remember the order of operations (PEMDAS/BODMAS) – Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction. This helps us solve these problems accurately every time!
b) 16 - 16 - 12 - 12 + 15 - 15
Next up, we have an interesting sequence of additions and subtractions. This problem looks tricky at first glance, but don't worry; it’s simpler than you think! We'll use the power of organization and basic arithmetic to solve it. Remember, the key is to take it step by step and not rush through the calculations. So, let's jump in and see how we can simplify this expression!
Notice that some numbers appear with both positive and negative signs. This is a great opportunity to simplify by combining like terms. Let's rewrite the expression to group the terms:
(16 - 16) + (-12 - 12) + (15 - 15)
Now, let's perform the operations within each group:
- 16 - 16 = 0
- -12 - 12 = -24
- 15 - 15 = 0
Substitute these values back into the expression:
0 + (-24) + 0
Now, simply add these numbers together:
0 - 24 + 0 = -24
Therefore, 16 - 16 - 12 - 12 + 15 - 15 = -24.
See, guys? By grouping like terms, we made this problem super manageable!
c) 8 * 8 * 2 - 2 * 2 - 2
Now, let's tackle a problem that combines multiplication and subtraction, giving us a chance to practice using powers again! This is where we'll really see the power of exponents in action. We're going to rewrite the expression using powers, making it easier to calculate and understand. Remember, breaking down complex problems into smaller steps is the key to success. So, let's dive in and show this problem who's boss!
First, let's rewrite the expression using powers:
- 8 * 8 can be written as 82 (8 squared)
- 2 * 2 can be written as 22 (2 squared)
So, the expression becomes: 82 * 2 - 22 - 2.
Now, let's calculate the powers:
- 82 = 8 * 8 = 64
- 22 = 2 * 2 = 4
Substitute these values back into the expression:
64 * 2 - 4 - 2
Now, follow the order of operations (PEMDAS/BODMAS). First, perform the multiplication:
64 * 2 = 128
Substitute this value back into the expression:
128 - 4 - 2
Now, perform the subtractions from left to right:
- 128 - 4 = 124
- 124 - 2 = 122
Therefore, 8 * 8 * 2 - 2 * 2 - 2 = 122.
Guys, always remember to follow the order of operations. It’s the secret sauce to getting the right answer every time!
d) 11 - 11 + 1 - 1 - 1 - 1 - 10 - 10
Last but not least, we have another problem involving additions and subtractions. This one might seem a bit long, but don't let that intimidate you! We're going to use the same techniques we used before: grouping like terms and simplifying step by step. By staying organized, we can easily find the solution. So, let's jump in and see how this one unfolds!
Similar to the previous problem, let's group the like terms:
(11 - 11) + (1 - 1 - 1 - 1) + (-10 - 10)
Now, perform the operations within each group:
- 11 - 11 = 0
- 1 - 1 - 1 - 1 = -2
- -10 - 10 = -20
Substitute these values back into the expression:
0 + (-2) + (-20)
Now, add these numbers together:
0 - 2 - 20 = -22
Therefore, 11 - 11 + 1 - 1 - 1 - 1 - 10 - 10 = -22.
Guys, we did it! We've solved all the problems step by step. Remember, practice makes perfect, so keep working on these types of problems, and you'll become a math whiz in no time!
Conclusion
We've successfully tackled a series of math problems involving powers and basic arithmetic operations. By breaking down each problem into manageable steps and remembering the order of operations, we were able to find the correct solutions. I hope this guide has been helpful and has made math a little less daunting and a lot more fun. Keep practicing, keep exploring, and most importantly, keep enjoying the journey of learning! You guys rock!