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Chapter 2: Problem 346

In the following exercises, simplify. $$ (7+5)^{2} $$

Short Answer

Expert verified
144

Step by step solution

01

Add the numbers inside the parentheses

First, add the numbers inside the parentheses. Here we have (7+5). Calculate 7+5.
02

Calculate the sum

The sum of 7 and 5 is 12.
03

Apply the exponent

Now apply the exponent outside the parentheses. We have (12)^2.
04

Simplify the exponentiation

Calculate 12^2. This means multiplying 12 by itself. 12 multiplied by 12 equals 144.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition
Let's begin with the basics of addition because it's essential for simplifying expressions. Addition is one of the four fundamental arithmetic operations where two or more numbers, called addends, are combined to get a sum. For instance, in our exercise, we need to add 7 and 5. Here鈥檚 how we do it:

We start with: 7 + 5.

Adding these numbers together, we get 12.

Addition might seem simple, but it's crucial to do it correctly, especially when it's part of a larger equation.
Exponentiation
Now, let's talk about exponentiation. Exponentiation is a mathematical operation that involves raising a number (the base) to the power of an exponent. In simpler terms, it means multiplying the base by itself a certain number of times indicated by the exponent. For instance, in the expression (12)^2:

- The base is 12
- The exponent is 2

So, (12)^2 means you multiply 12 by itself: 12 * 12 = 144.

This can seem tricky at first, but breaking it down can make it easier to understand!
Order of Operations
The order of operations is a critical concept in math to make sure we solve expressions correctly. It's often remembered by the acronym PEMDAS:

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


In our exercise, we follow PEMDAS. We first address the parentheses (7+5) which we already handled. Next, we move on to the exponentiation, taking our sum of 12 and raising it to the power of 2, simplifying to 144. Each step matters to make sure we reach the right answer!

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