Select The Correct Answer.Which Is The Correct Solution To The Expression $3 + 5^{\wedge} 2$? You Can Use A Calculator To Find The Answer.A. 10 B. 13 C. 28 D. 64

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Understanding the Expression

The given expression is $3 + 5^{\wedge} 2$. To solve this, we need to follow the order of operations (PEMDAS):

  1. Parentheses: There are no parentheses in the expression.
  2. Exponents: The exponent is 5^{\wedge} 2, which means 5 squared.
  3. Multiplication and Division: There are no multiplication or division operations in the expression.
  4. Addition and Subtraction: The expression ends with an addition operation.

Solving the Exponent

To solve the exponent, we need to calculate 5 squared, which is 5 * 5 = 25.

Adding 3 to the Result

Now that we have the result of the exponent, we can add 3 to it: 25 + 3 = 28.

Conclusion

Therefore, the correct solution to the expression $3 + 5^{\wedge} 2$ is 28.

Why is this Important?

Understanding the order of operations and how to solve expressions with exponents is crucial in mathematics. It helps us to evaluate expressions accurately and make informed decisions in various fields, such as science, engineering, and finance.

Real-World Applications

The concept of exponents and order of operations is used in many real-world applications, such as:

  • Finance: Calculating interest rates and investments.
  • Science: Measuring the growth of populations and chemical reactions.
  • Engineering: Designing and building structures, such as bridges and buildings.

Common Mistakes

When solving expressions with exponents, it's common to make mistakes, such as:

  • Forgetting to follow the order of operations.
  • Not evaluating the exponent correctly.
  • Not adding or subtracting correctly.

Tips and Tricks

To avoid making mistakes when solving expressions with exponents, follow these tips:

  • Read the expression carefully.
  • Follow the order of operations.
  • Evaluate the exponent correctly.
  • Check your work.

Conclusion

In conclusion, solving the expression $3 + 5^{\wedge} 2$ requires following the order of operations and evaluating the exponent correctly. By understanding the concept of exponents and order of operations, we can make informed decisions in various fields and avoid common mistakes.

Final Answer

The final answer is: 28

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:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  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: How do I evaluate an exponent?

A: To evaluate an exponent, you need to multiply the base number by itself as many times as the exponent indicates. For example:

  • 2^3 = 2 × 2 × 2 = 8
  • 3^2 = 3 × 3 = 9
  • 4^4 = 4 × 4 × 4 × 4 = 256

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:

  • 2^3 is read as "2 to the power of 3"
  • 3^2 is read as "3 squared"

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

A: To simplify an expression with multiple exponents, you need to follow the order of operations and evaluate each exponent separately. For example:

  • 2^3 × 2^2 = (2^3) × (2^2) = 8 × 4 = 32
  • 3^2 + 3^1 = (3^2) + (3^1) = 9 + 3 = 12

Q: Can I use a calculator to evaluate expressions with exponents?

A: Yes, you can use a calculator to evaluate expressions with exponents. However, make sure to follow the order of operations and enter the expression correctly. For example:

  • To evaluate 2^3, enter 2^3 into the calculator and press the equals button.
  • To evaluate 3^2, enter 3^2 into the calculator and press the equals button.

Q: What are some common mistakes to avoid when solving expressions with exponents?

A: Some common mistakes to avoid when solving expressions with exponents include:

  • Forgetting to follow the order of operations.
  • Not evaluating the exponent correctly.
  • Not adding or subtracting correctly.
  • Not checking your work.

Q: How can I practice solving expressions with exponents?

A: You can practice solving expressions with exponents by:

  • Working through practice problems in a textbook or online resource.
  • Using a calculator to evaluate expressions with exponents.
  • Creating your own expressions with exponents and solving them.
  • Asking a teacher or tutor for help.

Q: What are some real-world applications of expressions with exponents?

A: Expressions with exponents have many real-world applications, including:

  • Finance: Calculating interest rates and investments.
  • Science: Measuring the growth of populations and chemical reactions.
  • Engineering: Designing and building structures, such as bridges and buildings.

Q: Can I use expressions with exponents to solve problems in other areas of mathematics?

A: Yes, expressions with exponents can be used to solve problems in other areas of mathematics, including:

  • Algebra: Solving equations and inequalities with exponents.
  • Geometry: Calculating the area and perimeter of shapes with exponents.
  • Trigonometry: Solving trigonometric equations and identities with exponents.