Not evaluating the exponent first

Oct 13, 2025 by miodeya.com 30 views

Understanding the Expression

When simplifying the expression $2 - 3 \times 3^3$ , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). In this case, we have an exponent and a multiplication operation that needs to be evaluated before we can subtract the result from 2.

Evaluating the Exponent

The first step is to evaluate the exponent $3^3$ . This means multiplying 3 by itself three times: $3^3 = 3 \times 3 \times 3 = 27$ .

Evaluating the Multiplication

Next, we need to evaluate the multiplication $3 \times 27$ . This is a straightforward operation: $3 \times 27 = 81$ .

Simplifying the Expression

Now that we have evaluated the exponent and the multiplication, we can simplify the expression by substituting the results back into the original expression: $2 - 3 \times 3^3 = 2 - 81$ .

Final Answer

The final answer is $-79$ .

Why PEMDAS Matters

PEMDAS is a crucial concept in mathematics that helps us evaluate expressions in the correct order. Without it, we might get confused and make mistakes when simplifying expressions. By following the order of operations, we can ensure that our calculations are accurate and reliable.

Real-World Applications

Understanding how to simplify expressions like $2 - 3 \times 3^3$ is essential in many real-world applications, such as:

Science and Engineering: In scientific and engineering applications, we often need to evaluate complex expressions that involve exponents, multiplication, and subtraction. By following the order of operations, we can ensure that our calculations are accurate and reliable.
Finance: In finance, we often need to evaluate expressions that involve exponents, multiplication, and subtraction. By following the order of operations, we can ensure that our calculations are accurate and reliable.
Computer Programming: In computer programming, we often need to evaluate expressions that involve exponents, multiplication, and subtraction. By following the order of operations, we can ensure that our calculations are accurate and reliable.

Common Mistakes

When simplifying expressions like $2 - 3 \times 3^3$ , we often make mistakes by not following the order of operations. Some common mistakes include:

Not evaluating the exponent first: We might forget to evaluate the exponent $3^3$ before multiplying it by 3.
Not multiplying the numbers correctly: We might make a mistake when multiplying 3 by 27.
Not subtracting the result correctly: We might forget to subtract the result of the multiplication from 2.

Conclusion

Simplifying expressions like $2 - 3 \times 3^3$ requires us to follow the order of operations, often remembered by the acronym PEMDAS. By evaluating the exponent and the multiplication correctly, we can ensure that our calculations are accurate and reliable. In this article, we have discussed the importance of PEMDAS, real-world applications, and common mistakes. By following the order of operations, we can simplify expressions like $2 - 3 \times 3^3$ with confidence.

Additional Resources

For more information on simplifying expressions and the order of operations, check out the following resources:

Mathway: A math problem solver that can help you evaluate expressions and solve equations.
Khan Academy: A free online resource that provides video lessons and practice exercises on mathematics, including the order of operations.
Wolfram Alpha: A computational knowledge engine that can help you evaluate expressions and solve equations.

Final Thoughts

Simplifying expressions like $2 - 3 \times 3^3$ is an essential skill in mathematics that requires us to follow the order of operations. By understanding the importance of PEMDAS, we can ensure that our calculations are accurate and reliable. Whether you are a student, a teacher, or a professional, understanding how to simplify expressions is crucial in many real-world applications.

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about simplifying expressions like $2 - 3 \times 3^3$ .

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 simplifying an expression. The acronym PEMDAS is often used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponents next (such as squaring or cubing).
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: Why is it important to follow the order of operations?

A: Following the order of operations is crucial to ensure that our calculations are accurate and reliable. If we don't follow the order of operations, we might get confused and make mistakes when simplifying expressions.

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

A: An exponent is a small number that is raised to a power. For example, in the expression $3^3$ , the 3 is the base and the 3 is the exponent. The power is the result of raising the base to the exponent, which is 27 in this case.

Q: How do I evaluate an exponent?

A: To evaluate an exponent, you simply multiply the base by itself as many times as the exponent indicates. For example, to evaluate $3^3$ , you would multiply 3 by itself three times: $3 \times 3 \times 3 = 27$ .

Q: What is the difference between multiplication and exponentiation?

A: Multiplication is the operation of adding a number a certain number of times. For example, $3 \times 4$ means adding 3 together 4 times: $3 + 3 + 3 + 3 = 12$ . Exponentiation is the operation of raising a number to a power. For example, $3^4$ means multiplying 3 by itself 4 times: $3 \times 3 \times 3 \times 3 = 81$ .

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

A: To simplify an expression with multiple operations, you need to follow the order of operations. First, evaluate any exponents, then any multiplication and division operations, and finally any addition and subtraction operations.

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

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

Not evaluating the exponent first
Not multiplying the numbers correctly
Not subtracting the result correctly
Not following the order of operations

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through math problems and exercises. You can also use online resources such as math problem solvers and practice websites to help you improve your skills.

Additional Resources

For more information on simplifying expressions and the order of operations, check out the following resources:

Mathway: A math problem solver that can help you evaluate expressions and solve equations.
Khan Academy: A free online resource that provides video lessons and practice exercises on mathematics, including the order of operations.
Wolfram Alpha: A computational knowledge engine that can help you evaluate expressions and solve equations.