Evaluate The Expression 12 2 − ( 9 − 7 ) 3 + 6 12^2-(9-7)^3+6 1 2 2 − ( 9 − 7 ) 3 + 6 .${ \begin{aligned} 12 2-(9-7) 3+6 & = 12 2-(2) 3+6 \ & = \square - \square + 6 \end{aligned} }$

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves substituting values for variables and performing the operations in the correct order. In this article, we will evaluate the expression 122−(9−7)3+612^2-(9-7)^3+6 using the order of operations.

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

Let's evaluate the expression 122−(9−7)3+612^2-(9-7)^3+6 using the order of operations.

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the parentheses is (9−7)(9-7). We need to evaluate this expression first.

(9 - 7) = 2

So, the expression becomes 122−(2)3+612^2-(2)^3+6.

Step 2: Evaluate Exponential Expressions

Next, we need to evaluate the exponential expressions 12212^2 and (2)3(2)^3.

12^2 = 144
(2)^3 = 8

So, the expression becomes 144−8+6144-8+6.

Step 3: Evaluate Multiplication and Division Operations

There are no multiplication or division operations in this expression, so we can move on to the next step.

Step 4: Evaluate Addition and Subtraction Operations

Finally, we need to evaluate the addition and subtraction operations from left to right.

144 - 8 = 136
136 + 6 = 142

So, the final value of the expression is 142142.

Conclusion

Evaluating expressions is an essential skill in mathematics. By following the order of operations, we can ensure that we perform the operations in the correct order and obtain the correct result. In this article, we evaluated the expression 122−(9−7)3+612^2-(9-7)^3+6 using the order of operations and obtained a final value of 142142.

Common Mistakes to Avoid

When evaluating expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations: Make sure to evaluate expressions inside parentheses first, then exponents, then multiplication and division, and finally addition and subtraction.
  • Not evaluating expressions inside parentheses: Make sure to evaluate expressions inside parentheses before moving on to the next step.
  • Not checking for errors: Double-check your work to ensure that you haven't made any mistakes.

Practice Problems

Here are some practice problems to help you evaluate expressions:

  1. Evaluate the expression 32−(2)3+43^2-(2)^3+4.
  2. Evaluate the expression 12−(9−7)2+612-(9-7)^2+6.
  3. Evaluate the expression 23−(3−2)2+52^3-(3-2)^2+5.

Answer Key

  1. 32−(2)3+4=9−8+4=53^2-(2)^3+4 = 9-8+4 = 5
  2. 12−(9−7)2+6=12−4+6=1412-(9-7)^2+6 = 12-4+6 = 14
  3. 23−(3−2)2+5=8−1+5=122^3-(3-2)^2+5 = 8-1+5 = 12

Final Thoughts

Introduction

In our previous article, we evaluated the expression 122−(9−7)3+612^2-(9-7)^3+6 using the order of operations. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, 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 crucial to ensure that you obtain the correct result when evaluating an expression. If you don't follow the order of operations, you may get a different result, which can lead to errors in calculations.

Q: What happens if there are no parentheses in an expression?

A: If there are no parentheses in an expression, you can skip this step and move on to the next one. However, if there are any parentheses, you need to evaluate the expression inside the parentheses first.

Q: What happens if there are multiple exponents in an expression?

A: If there are multiple exponents in an expression, you need to evaluate them from left to right. For example, in the expression 23×322^3 \times 3^2, you need to evaluate 232^3 first, which equals 8, and then multiply it by 323^2, which equals 9.

Q: What happens if there are multiple multiplication and division operations in an expression?

A: If there are multiple multiplication and division operations in an expression, you need to evaluate them from left to right. For example, in the expression 12÷3×212 \div 3 \times 2, you need to evaluate 12÷312 \div 3 first, which equals 4, and then multiply it by 2.

Q: What happens if there are multiple addition and subtraction operations in an expression?

A: If there are multiple addition and subtraction operations in an expression, you need to evaluate them from left to right. For example, in the expression 12+3−212 + 3 - 2, you need to evaluate 12+312 + 3 first, which equals 15, and then subtract 2.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions. However, it's always a good idea to double-check your work to ensure that you haven't made any mistakes.

Q: How can I practice evaluating expressions?

A: You can practice evaluating expressions by working on practice problems, such as the ones listed below:

  1. Evaluate the expression 32−(2)3+43^2-(2)^3+4.
  2. Evaluate the expression 12−(9−7)2+612-(9-7)^2+6.
  3. Evaluate the expression 23−(3−2)2+52^3-(3-2)^2+5.

Practice Problems

Here are some practice problems to help you evaluate expressions:

  1. Evaluate the expression 42−(3)3+24^2-(3)^3+2.
  2. Evaluate the expression 12−(8−6)2+412-(8-6)^2+4.
  3. Evaluate the expression 33−(2)2+53^3-(2)^2+5.

Answer Key

  1. 42−(3)3+2=16−27+2=−94^2-(3)^3+2 = 16-27+2 = -9
  2. 12−(8−6)2+4=12−4+4=1212-(8-6)^2+4 = 12-4+4 = 12
  3. 33−(2)2+5=27−4+5=283^3-(2)^2+5 = 27-4+5 = 28

Final Thoughts

Evaluating expressions is a crucial skill in mathematics. By following the order of operations and practicing regularly, you can become more confident and proficient in mathematics. Remember to always double-check your work to ensure that you haven't made any mistakes.