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Chapter 5: Problem 71

For Exercises \(71-82,\) simplify by using the order of operations. $$(3.7-1.2)^{2}$$

Short Answer

Expert verified
6.25

Step by step solution

01

Parentheses

First, solve the expression inside the parentheses. Calculate the value of \(3.7 - 1.2\).
02

Subtraction

Perform the subtraction: \(3.7 - 1.2 = 2.5\).
03

Exponentiation

Next, raise the result to the power of 2. Calculate \((2.5)^{2}\).
04

Final Calculation

Complete the exponentiation: \((2.5)^{2} = 6.25\).

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Key Concepts

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

Parentheses
When simplifying mathematical expressions, the first step is to handle any calculations inside parentheses. Parentheses are used to group parts of an expression that should be considered as a single unit. In our exercise, we have \(3.7 - 1.2\). This tells us to perform the operation inside the parentheses before addressing any other operations outside them.
By solving the expression inside the parentheses first, we ensure accurate results. If we skipped this step, it might lead to a completely different outcome. So, always look for parentheses and solve those parts first.
Subtraction
Next, after addressing parentheses, we move on to any subtraction or addition within them. Subtraction is just the process of taking one number away from another. In our example, after solving the parentheses, we performed the subtraction \(3.7 - 1.2\).
Subtraction is straightforward, but ensure to line up the decimal points when you are dealing with decimal numbers. This helps in minimizing mistakes. The result we got here was \(2.5\). Subtracting accurately is crucial because any mistake here will carry over to the next steps.
Exponentiation
Exponentiation involves raising a number to the power of another number. It means multiplying the base number by itself as many times as the exponent indicates. For example, \(2.5^{2}\) means \(2.5 \times 2.5\). In our problem, after subtraction, we need to raise \(2.5\) to the power of 2.
This operation is crucial in many areas of math and science. Calculators can help with larger exponents, but understanding the concept is key to mastering higher-level math.
Simplification
Simplification is about reducing an expression to its most basic form. After dealing with parentheses, subtraction, and exponentiation, the final step is to put it all together. For our example, we completed the exponentiation to get \(6.25\).
Simplification ensures we have the most streamlined and understandable version of our original expression. It's the process of tidying up our work to present the cleanest and most accurate solution possible.

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Most popular questions from this chapter

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