What Is The Value Of The Expression Below? 2 [ 3 ( 4 2 + 1 ) ] − 2 3 2\left[3\left(4^2+1\right)\right]-2^3 2 [ 3 ( 4 2 + 1 ) ] − 2 3 A. 156 B. 110 C. 94 D. 48

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Understanding the Expression

The given expression is 2[3(42+1)]−232\left[3\left(4^2+1\right)\right]-2^3. To find the value of this expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses.
  2. Evaluate any exponential expressions.
  3. Multiply and divide from left to right.
  4. Add and subtract from left to right.

Step 1: Evaluate the Expressions Inside the Parentheses

The expression inside the parentheses is 42+14^2+1. To evaluate this expression, we need to follow the order of operations:

  1. Evaluate the exponential expression 424^2.
  2. Add 1 to the result.

42=164^2 = 16

16+1=1716 + 1 = 17

So, the expression inside the parentheses is equal to 17.

Step 2: Evaluate the Exponential Expression

The expression is 232^3. To evaluate this expression, we need to raise 2 to the power of 3:

23=82^3 = 8

Step 3: Multiply and Divide from Left to Right

The expression is 2[3(42+1)]2\left[3\left(4^2+1\right)\right]. To evaluate this expression, we need to multiply 2 by the result of the expression inside the parentheses:

2[3(42+1)]=2[3(17)]2\left[3\left(4^2+1\right)\right] = 2\left[3\left(17\right)\right]

2[3(17)]=2(51)2\left[3\left(17\right)\right] = 2\left(51\right)

2(51)=1022\left(51\right) = 102

Step 4: Add and Subtract from Left to Right

The expression is 2(51)−232\left(51\right) - 2^3. To evaluate this expression, we need to subtract 8 from 102:

102−8=94102 - 8 = 94

Conclusion

The value of the expression 2[3(42+1)]−232\left[3\left(4^2+1\right)\right]-2^3 is 94.

Answer

The correct answer is C. 94.

Discussion

This problem requires the application of the order of operations (PEMDAS) to evaluate the expression. The expression inside the parentheses is evaluated first, followed by the exponential expression, and then the multiplication and division operations. Finally, the addition and subtraction operations are performed to obtain the final result.

Related Problems

  • Evaluate the expression 3(22+1)−233\left(2^2+1\right)-2^3.
  • Evaluate the expression 4(32+1)−334\left(3^2+1\right)-3^3.
  • Evaluate the expression 5(22+1)−235\left(2^2+1\right)-2^3.

Practice Problems

  • Evaluate the expression 2(32+1)−332\left(3^2+1\right)-3^3.
  • Evaluate the expression 3(42+1)−433\left(4^2+1\right)-4^3.
  • Evaluate the expression 4(22+1)−234\left(2^2+1\right)-2^3.

Solutions

  • Evaluate the expression 2(32+1)−332\left(3^2+1\right)-3^3:
    • Evaluate the expression inside the parentheses: 32+1=103^2+1 = 10
    • Multiply 2 by the result: 2(10)=202\left(10\right) = 20
    • Subtract 27 from the result: 20−27=−720 - 27 = -7
  • Evaluate the expression 3(42+1)−433\left(4^2+1\right)-4^3:
    • Evaluate the expression inside the parentheses: 42+1=174^2+1 = 17
    • Multiply 3 by the result: 3(17)=513\left(17\right) = 51
    • Subtract 64 from the result: 51−64=−1351 - 64 = -13
  • Evaluate the expression 4(22+1)−234\left(2^2+1\right)-2^3:
    • Evaluate the expression inside the parentheses: 22+1=52^2+1 = 5
    • Multiply 4 by the result: 4(5)=204\left(5\right) = 20
    • Subtract 8 from the result: 20−8=1220 - 8 = 12
      Q&A: Understanding the Value of Expressions =============================================

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:

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

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between an exponent and a power?

A: An exponent and a power are often used interchangeably, but technically, an exponent is the number that is raised to a power. For example, in the expression 232^3, the 3 is the exponent and the 2 is the base.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, we need to raise the base to the power of the exponent. For example, in the expression 232^3, we need to raise 2 to the power of 3.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication involves adding a number a certain number of times, while division involves finding the quotient of two numbers.

Q: How do I evaluate multiplication and division operations?

A: To evaluate multiplication and division operations, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then any multiplication and division operations from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different rules. Addition involves combining two or more numbers, while subtraction involves finding the difference between two numbers.

Q: How do I evaluate addition and subtraction operations?

A: To evaluate addition and subtraction operations, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations from left to right.

Q: What is the value of the expression 2[3(42+1)]−232\left[3\left(4^2+1\right)\right]-2^3?

A: To evaluate this expression, we need to follow the order of operations (PEMDAS). We start by evaluating the expression inside the parentheses, which is 42+14^2+1. This expression is equal to 17. Then, we multiply 3 by 17 to get 51. Next, we multiply 2 by 51 to get 102. Finally, we subtract 8 from 102 to get 94.

Q: What is the value of the expression 3(22+1)−233\left(2^2+1\right)-2^3?

A: To evaluate this expression, we need to follow the order of operations (PEMDAS). We start by evaluating the expression inside the parentheses, which is 22+12^2+1. This expression is equal to 5. Then, we multiply 3 by 5 to get 15. Next, we subtract 8 from 15 to get 7.

Q: What is the value of the expression 4(32+1)−334\left(3^2+1\right)-3^3?

A: To evaluate this expression, we need to follow the order of operations (PEMDAS). We start by evaluating the expression inside the parentheses, which is 32+13^2+1. This expression is equal to 10. Then, we multiply 4 by 10 to get 40. Next, we subtract 27 from 40 to get 13.

Q: What is the value of the expression 5(22+1)−235\left(2^2+1\right)-2^3?

A: To evaluate this expression, we need to follow the order of operations (PEMDAS). We start by evaluating the expression inside the parentheses, which is 22+12^2+1. This expression is equal to 5. Then, we multiply 5 by 5 to get 25. Next, we subtract 8 from 25 to get 17.

Conclusion

In this article, we have discussed the order of operations (PEMDAS) and how to evaluate expressions using this rule. We have also answered some common questions about the order of operations and provided examples of how to evaluate expressions using this rule.