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Chapter 5: Problem 75

Simplify the given expression. \(6.3-4.2(9.3)^{2}\)

Short Answer

Expert verified
The simplified expression is -356.958.

Step by step solution

01

Evaluate the Exponent

Calculate the square of 9.3. \( (9.3)^2 = 9.3 \times 9.3 = 86.49 \)
02

Multiply by 4.2

Multiply the result from Step 1 by 4.2. \( 4.2 \times 86.49 = 363.258 \)
03

Subtract from 6.3

Subtract the result from Step 2 from 6.3. \( 6.3 - 363.258 = -356.958 \)

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Key Concepts

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

Understanding the Order of Operations
When simplifying mathematical expressions, it is crucial to follow the correct order of operations known as PEMDAS. This acronym stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Each type of operation is performed in a specific sequence to ensure that the expression is simplified correctly.
  • Start with operations inside Parentheses.
  • Evaluate Exponents.
  • Perform Multiplication and Division from left to right.
  • Finally, do Addition and Subtraction from left to right.

In the given expression \(6.3-4.2(9.3)^{2}\), following the order of operations ensures accurate results. The exponent is solved first, followed by multiplication, and finally subtraction.
Performing Arithmetic Operations
Arithmetic operations form the basis of many mathematical problems and include addition, subtraction, multiplication, and division. When simplifying expressions, knowing when to perform each operation is crucial.

In the present exercise, we encounter different operations:
  • Multiplication: We see this in 4.2 multiplied by the result of \((9.3)^2\).
  • Subtraction: This is applied when we subtract the product of 4.2 and \((9.3)^2\) from 6.3.

By adhering closely to the order of operations, you can accurately carry out these operations step-by-step without confusion.
Working with Exponents
Exponents are a key part of mathematical calculations that represent the number of times a number is multiplied by itself. For instance, the expression \((9.3)^2\) means 9.3 is multiplied by itself once. It is like saying "9.3 squared."

  • Calculate exponents first when simplifying expressions after handling parentheses.
  • In the expression \((9.3)^2\), you'll calculate it as 9.3 times 9.3, giving the result of 86.49 as shown in the solution steps.

Understanding exponents is vital because they can significantly affect the outcome of an expression. Handle them carefully and early on in the order of operations to simplify complex expressions accurately.

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Most popular questions from this chapter

Compute the exact square root. \(\sqrt{\frac{529}{16}}\)

Your solutions should include a well-labeled sketch. The length of one leg of a right triangle is 6 meters, and the length of the hypotenuse is 10 meters. Find the exact length of the other leg.

Compute the exact square root. If the square root is undefined, write "undefined". \(\sqrt{-256}\)

Compute the exact value of the given expression. \(-2 \sqrt{324}-6 \sqrt{361}\)

Your solutions should include a well-labeled sketch. The lengths of two legs of a right triangle are 7 meters and 8 meters. Find the exact length of the hypotenuse.
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