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Chapter 5: Problem 72

For Exercises \(71-82,\) simplify by using the order of operations. $$(6.8-4.7)^{2}$$

Short Answer

Expert verified
4.41

Step by step solution

01

- Parentheses

First, solve the expression within the parentheses. Calculate the difference between 6.8 and 4.7:\( 6.8 - 4.7 = 2.1 \)
02

- Exponentiation

Next, square the result from the parentheses. Raise 2.1 to the power of 2:\( (2.1)^2 = 4.41 \)

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Key Concepts

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

Parentheses
When solving mathematical expressions, the first step following the order of operations is to deal with parentheses. Parentheses are used to group parts of an equation that should be solved first.

For instance, in the problem \( (6.8 - 4.7)^2 \) given in the exercise, you need to calculate the expression inside the parentheses \(6.8 - 4.7 \) before doing anything else.

This means you subtract 4.7 from 6.8, which gives you 2.1. So the expression simplifies to \( (2.1)^2 \). Dealing with parentheses first simplifies the process and ensures accurate results in the following steps.
Exponentiation
The next step in the order of operations is exponentiation, which means raising a number to the power of another number.

After simplifying the expression within the parentheses to 2.1, we need to square it because of the exponent 2 attached to it.

Squaring means multiplying the number by itself, so \( 2.1 \times 2.1 = 4.41 \). This completes the exponentiation step for our exercise.
Simplify Expressions
Once you have followed the order of operations by handling parentheses and exponentiation, you are left with a simplified expression.

An expression is considered simplified when there are no further operations to perform.

In our case, after computing the square of 2.1 to get 4.41, no additional calculations are needed.
Therefore, the simplified form of the original expression \( (6.8 - 4.7)^2 \) is 4.41. By breaking down each step and following the precise order, we ensure accuracy and make complex expressions easier to manage.

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