Evaluate The Expression: \[$(6 + 5 - 9)^2\$\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression {(6 + 5 - 9)^2$}$. This expression involves addition, subtraction, and exponentiation. We will break down the expression step by step to simplify it and find its value.

Understanding the Expression

The given expression is {(6 + 5 - 9)^2$}$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: Evaluate any exponents (such as squaring a number).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is ${6 + 5 - 9\$}. To evaluate this expression, we need to follow the order of operations:

  1. Addition: Evaluate the addition operation first. ${6 + 5 = 11\$}
  2. Subtraction: Evaluate the subtraction operation next. ${11 - 9 = 2\$}

So, the expression inside the parentheses simplifies to ${2\$}.

Evaluating the Exponent

Now that we have simplified the expression inside the parentheses, we can evaluate the exponent. The expression is ${2^2\$}. To evaluate this expression, we need to square the number 2.

${2^2 = 4\$}

Conclusion

In conclusion, the expression {(6 + 5 - 9)^2$}$ simplifies to ${4\$}. We followed the order of operations to evaluate the expression step by step. First, we evaluated the expression inside the parentheses, and then we evaluated the exponent.

Importance of Evaluating Expressions

Evaluating expressions is an essential skill in mathematics. It helps us to simplify complex expressions and find their values. In real-world applications, evaluating expressions is used in various fields such as science, engineering, and finance. For example, in physics, we use expressions to calculate the distance traveled by an object, while in finance, we use expressions to calculate the interest on a loan.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

  • Follow the order of operations (PEMDAS).
  • Simplify the expression inside the parentheses first.
  • Evaluate any exponents next.
  • Finally, evaluate any multiplication and division operations from left to right.
  • Evaluate any addition and subtraction operations from left to right.

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating expressions:

  • Not following the order of operations (PEMDAS).
  • Not simplifying the expression inside the parentheses first.
  • Not evaluating any exponents next.
  • Not evaluating any multiplication and division operations from left to right.
  • Not evaluating any addition and subtraction operations from left to right.

Practice Problems

Here are some practice problems to help you evaluate expressions:

  • Evaluate the expression {(3 + 2 - 1)^2$}$.
  • Evaluate the expression {(4 - 2 + 1)^2$}$.
  • Evaluate the expression {(2 + 3 - 4)^2$}$.

Conclusion

In conclusion, evaluating expressions is an essential skill in mathematics. It helps us to simplify complex expressions and find their values. We followed the order of operations to evaluate the expression {(6 + 5 - 9)^2$}$ step by step. We simplified the expression inside the parentheses, evaluated the exponent, and finally found the value of the expression. We also provided some tips and common mistakes to avoid when evaluating expressions.

Introduction

In our previous article, we evaluated the expression {(6 + 5 - 9)^2$}$ step by step. We followed the order of operations (PEMDAS) to simplify the expression and find its value. In this article, we will answer some frequently asked questions (FAQs) related to evaluating expressions.

Q&A

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate the expression inside the parentheses first.
  • Exponents: Evaluate any exponents (such as squaring a number) next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Evaluate any 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 important because it ensures that we perform the operations in the correct order. If we don't follow the order of operations, we may get the wrong answer.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, we need to follow the order of operations. We start by evaluating the expression inside the parentheses, then we evaluate any exponents, and finally we evaluate any multiplication and division operations from left to right.

Q: What is the difference between an expression and an equation?

A: An expression is a combination of numbers, variables, and mathematical operations. An equation is a statement that says two expressions are equal. For example, ${2x + 3 = 5\$} is an equation, while ${2x + 3\$} is an expression.

Q: How do I simplify an expression?

A: To simplify an expression, we need to combine like terms and eliminate any unnecessary operations. We can also use the order of operations to simplify an expression.

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

A: Some common mistakes to avoid when evaluating expressions include:

  • Not following the order of operations (PEMDAS).
  • Not simplifying the expression inside the parentheses first.
  • Not evaluating any exponents next.
  • Not evaluating any multiplication and division operations from left to right.
  • Not evaluating any addition and subtraction operations from left to right.

Q: How do I practice evaluating expressions?

A: To practice evaluating expressions, you can try solving some practice problems. You can also use online resources such as math websites and apps to practice evaluating expressions.

Conclusion

In conclusion, evaluating expressions is an essential skill in mathematics. We followed the order of operations to evaluate the expression {(6 + 5 - 9)^2$}$ step by step. We also answered some frequently asked questions (FAQs) related to evaluating expressions. We hope this article has been helpful in understanding how to evaluate expressions.

Practice Problems

Here are some practice problems to help you evaluate expressions:

  • Evaluate the expression {(3 + 2 - 1)^2$}$.
  • Evaluate the expression {(4 - 2 + 1)^2$}$.
  • Evaluate the expression {(2 + 3 - 4)^2$}$.

Resources

Here are some resources to help you learn more about evaluating expressions:

  • Khan Academy: Evaluating Expressions
  • Mathway: Evaluating Expressions
  • IXL: Evaluating Expressions

Conclusion

In conclusion, evaluating expressions is an essential skill in mathematics. We followed the order of operations to evaluate the expression {(6 + 5 - 9)^2$}$ step by step. We also answered some frequently asked questions (FAQs) related to evaluating expressions. We hope this article has been helpful in understanding how to evaluate expressions.