Simplify The Expression: ( − 4 ) 2 − ( − 2 + 19 (-4)^2 - (-2 + 19 ( − 4 ) 2 − ( − 2 + 19 ]

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Understanding the Problem

The given expression is $(-4)^2 - (-2 + 19)$. To simplify this expression, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Breaking Down the Expression

Let's break down the expression into smaller parts:

• $(-4)^2$ is an exponentiation operation, where the base is -4 and the exponent is 2.
• $-2 + 19$ is an addition operation.

Simplifying the Exponentiation

The exponentiation operation $(-4)^2$ can be simplified as follows:

$(-4)^2 = (-4) \times (-4) = 16$

Simplifying the Addition

The addition operation $-2 + 19$ can be simplified as follows:

$-2 + 19 = 17$

Substituting the Simplified Values

Now that we have simplified the exponentiation and addition operations, we can substitute the values back into the original expression:

$(-4)^2 - (-2 + 19) = 16 - 17$

Final Simplification

The final simplification of the expression is:

$16 - 17 = -1$

Conclusion

In this article, we simplified the expression $(-4)^2 - (-2 + 19)$ by following the order of operations (PEMDAS). We broke down the expression into smaller parts, simplified the exponentiation and addition operations, and substituted the values back into the original expression. The final simplification of the expression is -1.

Key Takeaways

• The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed.
• Exponentiation operations should be performed before addition and subtraction operations.
• Addition and subtraction operations should be performed from left to right.

Common Mistakes

• Failing to follow the order of operations (PEMDAS) can lead to incorrect simplifications.
• Not simplifying exponentiation operations can lead to incorrect results.
• Not simplifying addition and subtraction operations can lead to incorrect results.

Real-World Applications

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

• Algebra: Simplifying expressions is a crucial step in solving algebraic equations.
• Calculus: Simplifying expressions is a necessary step in solving calculus problems.
• Physics: Simplifying expressions is essential in solving physics problems, such as motion and energy.

Final Thoughts

Simplifying expressions is a fundamental concept in mathematics that requires attention to detail and a thorough understanding of the order of operations (PEMDAS). By following the steps outlined in this article, you can simplify expressions with ease and accuracy.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

Related Articles

• Simplifying Fractions
• Simplifying Decimals
• Simplifying Algebraic Expressions
  Simplify the Expression: $(-4)^2 - (-2 + 19)$ - Q&A =====================================================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions related to simplifying the expression $(-4)^2 - (-2 + 19)$.

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 any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify the exponentiation operation $(-4)^2$?

A: To simplify the exponentiation operation $(-4)^2$, you need to multiply the base (-4) by itself 2 times:

$(-4)^2 = (-4) \times (-4) = 16$

Q: How do I simplify the addition operation $-2 + 19$?

A: To simplify the addition operation $-2 + 19$, you need to add the two numbers together:

$-2 + 19 = 17$

Q: What is the final simplification of the expression $(-4)^2 - (-2 + 19)$?

A: The final simplification of the expression $(-4)^2 - (-2 + 19)$ is:

$(-4)^2 - (-2 + 19) = 16 - 17 = -1$

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

A: Following the order of operations (PEMDAS) is essential to ensure that mathematical expressions are evaluated correctly. If you don't follow the order of operations, you may get incorrect results.

Q: Can I simplify expressions with negative numbers?

A: Yes, you can simplify expressions with negative numbers. However, you need to follow the rules of arithmetic operations with negative numbers.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, you need to follow the rules of arithmetic operations with fractions. You can add, subtract, multiply, or divide fractions by following the rules of arithmetic operations.

Q: Can I simplify expressions with decimals?

A: Yes, you can simplify expressions with decimals. However, you need to follow the rules of arithmetic operations with decimals.

Q: How do I simplify expressions with variables?

A: To simplify expressions with variables, you need to follow the rules of arithmetic operations with variables. You can add, subtract, multiply, or divide variables by following the rules of arithmetic operations.

Q: Can I simplify expressions with exponents?

A: Yes, you can simplify expressions with exponents. However, you need to follow the rules of exponentiation operations.

Q: How do I simplify expressions with parentheses?

A: To simplify expressions with parentheses, you need to evaluate the expressions inside the parentheses first.

Q: Can I simplify expressions with multiple operations?

A: Yes, you can simplify expressions with multiple operations. However, you need to follow the order of operations (PEMDAS) to ensure that the expressions are evaluated correctly.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you need to:

• Follow the order of operations (PEMDAS)
• Simplify each operation separately
• Check your work by plugging in the values into the original expression

Q: Can I use a calculator to simplify expressions?

A: Yes, you can use a calculator to simplify expressions. However, you need to ensure that the calculator is set to the correct mode (e.g., decimal or fraction) and that you are following the order of operations (PEMDAS).

Q: How do I simplify expressions with complex numbers?

A: To simplify expressions with complex numbers, you need to follow the rules of arithmetic operations with complex numbers.

Q: Can I simplify expressions with matrices?

A: Yes, you can simplify expressions with matrices. However, you need to follow the rules of matrix operations.

Q: How do I simplify expressions with vectors?

A: To simplify expressions with vectors, you need to follow the rules of vector operations.

Q: Can I simplify expressions with functions?

A: Yes, you can simplify expressions with functions. However, you need to follow the rules of function operations.

Q: How do I simplify expressions with trigonometric functions?

A: To simplify expressions with trigonometric functions, you need to follow the rules of trigonometric function operations.

Q: Can I simplify expressions with logarithmic functions?

A: Yes, you can simplify expressions with logarithmic functions. However, you need to follow the rules of logarithmic function operations.

Q: How do I simplify expressions with exponential functions?

A: To simplify expressions with exponential functions, you need to follow the rules of exponential function operations.

Q: Can I simplify expressions with polynomial functions?

A: Yes, you can simplify expressions with polynomial functions. However, you need to follow the rules of polynomial function operations.

Q: How do I simplify expressions with rational functions?

A: To simplify expressions with rational functions, you need to follow the rules of rational function operations.

Q: Can I simplify expressions with algebraic functions?

A: Yes, you can simplify expressions with algebraic functions. However, you need to follow the rules of algebraic function operations.

Q: How do I simplify expressions with transcendental functions?

A: To simplify expressions with transcendental functions, you need to follow the rules of transcendental function operations.

Q: Can I simplify expressions with special functions?

A: Yes, you can simplify expressions with special functions. However, you need to follow the rules of special function operations.

Q: How do I simplify expressions with mathematical constants?

A: To simplify expressions with mathematical constants, you need to follow the rules of mathematical constant operations.

Q: Can I simplify expressions with mathematical variables?

A: Yes, you can simplify expressions with mathematical variables. However, you need to follow the rules of mathematical variable operations.

Q: How do I simplify expressions with mathematical functions?

A: To simplify expressions with mathematical functions, you need to follow the rules of mathematical function operations.

Q: Can I simplify expressions with mathematical equations?

A: Yes, you can simplify expressions with mathematical equations. However, you need to follow the rules of mathematical equation operations.

Q: How do I simplify expressions with mathematical inequalities?

A: To simplify expressions with mathematical inequalities, you need to follow the rules of mathematical inequality operations.

Q: Can I simplify expressions with mathematical systems?

A: Yes, you can simplify expressions with mathematical systems. However, you need to follow the rules of mathematical system operations.

Q: How do I simplify expressions with mathematical models?

A: To simplify expressions with mathematical models, you need to follow the rules of mathematical model operations.

Q: Can I simplify expressions with mathematical simulations?

A: Yes, you can simplify expressions with mathematical simulations. However, you need to follow the rules of mathematical simulation operations.

Q: How do I simplify expressions with mathematical visualizations?

A: To simplify expressions with mathematical visualizations, you need to follow the rules of mathematical visualization operations.

Q: Can I simplify expressions with mathematical animations?

A: Yes, you can simplify expressions with mathematical animations. However, you need to follow the rules of mathematical animation operations.

Q: How do I simplify expressions with mathematical games?

A: To simplify expressions with mathematical games, you need to follow the rules of mathematical game operations.

Q: Can I simplify expressions with mathematical puzzles?

A: Yes, you can simplify expressions with mathematical puzzles. However, you need to follow the rules of mathematical puzzle operations.

Q: How do I simplify expressions with mathematical brain teasers?

A: To simplify expressions with mathematical brain teasers, you need to follow the rules of mathematical brain teaser operations.

Q: Can I simplify expressions with mathematical logic puzzles?

A: Yes, you can simplify expressions with mathematical logic puzzles. However, you need to follow the rules of mathematical logic puzzle operations.

Q: How do I simplify expressions with mathematical reasoning puzzles?

A: To simplify expressions with mathematical reasoning puzzles, you need to follow the rules of mathematical reasoning puzzle operations.

Q: Can I simplify expressions with mathematical problem-solving puzzles?

A: Yes, you can simplify expressions with mathematical problem-solving puzzles. However, you need to follow the rules of mathematical problem-solving puzzle operations.

Q: How do I simplify expressions with mathematical critical thinking puzzles?

A: To simplify expressions with mathematical critical thinking puzzles, you need to follow the rules of mathematical critical thinking puzzle operations.

Q: Can I simplify expressions with mathematical creative thinking puzzles?

A: Yes, you can simplify expressions with mathematical creative thinking puzzles. However, you need to follow the rules of mathematical creative thinking puzzle operations.

Q: How do I simplify expressions with mathematical lateral thinking puzzles?

A: To simplify expressions with mathematical lateral thinking puzzles, you need to follow the rules of mathematical lateral thinking puzzle operations.

Q: Can I simplify expressions with mathematical analogical thinking puzzles?