4.2.2-3-(-2)(5) - (-4)³​

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Solving the Complex Expression: 4.2.2-3-(-2)(5) - (-4)³

In mathematics, expressions can become increasingly complex, involving multiple operations, variables, and even exponents. The given expression, 4.2.2-3-(-2)(5) - (-4)³, is a perfect example of such a complex expression. In this article, we will break down the expression, step by step, to simplify it and arrive at a final value.

Before we dive into solving the expression, let's first understand what it means. The expression consists of several parts:

  • 4.2.2-3: This is a simple subtraction operation.
  • -(-2)(5): This is a multiplication operation involving a negative number.
  • -(-4)³: This is an exponentiation operation involving a negative number.

Step 1: Simplify the Exponents

Let's start by simplifying the exponents in the expression. The exponentiation operation is -(-4)³. To simplify this, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: -4
  2. Raise -4 to the power of 3: (-4)³ = -64

So, the expression becomes: 4.2.2-3-(-2)(5) - (-64)

Step 2: Simplify the Multiplication

Next, let's simplify the multiplication operation: -(-2)(5). To simplify this, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: -2
  2. Multiply -2 by 5: -2(5) = -10

So, the expression becomes: 4.2.2-3-10 - (-64)

Step 3: Simplify the Subtraction

Now, let's simplify the subtraction operation: 4.2.2-3-10. To simplify this, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: 4.2.2-3
  2. Subtract 10 from the result: 4.2.2-3 - 10

To simplify 4.2.2-3, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: 4.2.2
  2. Subtract 3 from the result: 4.2.2 - 3 = 1.2.2

So, the expression becomes: 1.2.2 - 10 - (-64)

Step 4: Simplify the Final Expression

Now, let's simplify the final expression: 1.2.2 - 10 - (-64). To simplify this, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: -64
  2. Add 64 to the result: 1.2.2 - 10 + 64

To simplify 1.2.2, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: 1.2.2
  2. Add 64 to the result: 1.2.2 + 64 = 65.2.2

So, the expression becomes: 65.2.2 - 10

Step 5: Final Simplification

Finally, let's simplify the expression: 65.2.2 - 10. To simplify this, we need to follow the order of operations (PEMDAS):

  1. Subtract 10 from the result: 65.2.2 - 10 = 55.2.2

In conclusion, the complex expression 4.2.2-3-(-2)(5) - (-4)³ can be simplified by following the order of operations (PEMDAS). By breaking down the expression into smaller parts and simplifying each part step by step, we arrive at a final value of 55.2.2.

  • The order of operations (PEMDAS) is crucial in simplifying complex expressions.
  • Exponents should be evaluated first, followed by multiplication and division, and finally addition and subtraction.
  • Simplifying expressions step by step can help avoid errors and arrive at a final value.

The concept of simplifying complex expressions is essential in various real-world applications, such as:

  • Science and Engineering: Simplifying complex expressions is crucial in scientific and engineering calculations, where accuracy and precision are paramount.
  • Finance: Simplifying complex expressions is essential in financial calculations, such as calculating interest rates and investment returns.
  • Computer Programming: Simplifying complex expressions is crucial in computer programming, where efficient and accurate calculations are necessary.

In conclusion, simplifying complex expressions is a crucial skill in mathematics and various real-world applications. By following the order of operations (PEMDAS) and breaking down expressions into smaller parts, we can arrive at a final value and avoid errors.
Frequently Asked Questions: Simplifying Complex Expressions

In our previous article, we explored the concept of simplifying complex expressions, including the expression 4.2.2-3-(-2)(5) - (-4)³. In this article, we will address some of the most frequently asked questions related to simplifying complex expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate exponents next.
  • Multiplication and Division: Evaluate multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is crucial in simplifying complex expressions and avoiding errors. By following the order of operations, we can ensure that mathematical operations are performed in the correct order, resulting in accurate and reliable calculations.

Q: How do I simplify complex expressions with multiple operations?

A: To simplify complex expressions with multiple operations, follow these steps:

  1. Identify the operations in the expression, including addition, subtraction, multiplication, and division.
  2. Evaluate expressions inside parentheses first.
  3. Evaluate exponents next.
  4. Evaluate multiplication and division operations from left to right.
  5. Finally, evaluate addition and subtraction operations from left to right.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol or expression that represents a value that can change. A constant, on the other hand, is a value that does not change.

Q: How do I simplify expressions with variables and constants?

A: To simplify expressions with variables and constants, follow these steps:

  1. Identify the variables and constants in the expression.
  2. Evaluate expressions inside parentheses first.
  3. Evaluate exponents next.
  4. Evaluate multiplication and division operations from left to right.
  5. Finally, evaluate addition and subtraction operations from left to right.

Q: Can I use a calculator to simplify complex expressions?

A: Yes, you can use a calculator to simplify complex expressions. However, it's essential to understand the order of operations and how to simplify expressions manually to ensure accuracy and reliability.

Q: What are some common mistakes to avoid when simplifying complex expressions?

A: Some common mistakes to avoid when simplifying complex expressions include:

  • Not following the order of operations.
  • Not evaluating expressions inside parentheses first.
  • Not evaluating exponents next.
  • Not evaluating multiplication and division operations from left to right.
  • Not evaluating addition and subtraction operations from left to right.

In conclusion, simplifying complex expressions is a crucial skill in mathematics and various real-world applications. By following the order of operations (PEMDAS) and breaking down expressions into smaller parts, we can arrive at a final value and avoid errors. We hope this article has addressed some of the most frequently asked questions related to simplifying complex expressions.

  • The order of operations (PEMDAS) is crucial in simplifying complex expressions.
  • Evaluating expressions inside parentheses first is essential.
  • Exponents should be evaluated next.
  • Multiplication and division operations should be evaluated from left to right.
  • Addition and subtraction operations should be evaluated from left to right.

The concept of simplifying complex expressions is essential in various real-world applications, such as:

  • Science and Engineering: Simplifying complex expressions is crucial in scientific and engineering calculations, where accuracy and precision are paramount.
  • Finance: Simplifying complex expressions is essential in financial calculations, such as calculating interest rates and investment returns.
  • Computer Programming: Simplifying complex expressions is crucial in computer programming, where efficient and accurate calculations are necessary.

In conclusion, simplifying complex expressions is a crucial skill in mathematics and various real-world applications. By following the order of operations (PEMDAS) and breaking down expressions into smaller parts, we can arrive at a final value and avoid errors.