Select The Correct Answer.What Is $10^0 + 10^1 + 10^2$ Equal To?A. 10,201 B. 120 C. 111 D. 110 E. 100

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Introduction

In mathematics, exponential expressions are a fundamental concept that helps us understand the behavior of numbers raised to a power. In this article, we will delve into the world of exponential expressions and explore the concept of $10^0 + 10^1 + 10^2$. We will examine the properties of exponents, learn how to evaluate these expressions, and finally, determine the correct answer among the given options.

What are Exponents?

Exponents are a shorthand way of representing repeated multiplication. For example, $2^3$ can be read as "2 to the power of 3" or "2 cubed". This means that $2^3 = 2 \times 2 \times 2 = 8$. Exponents are a powerful tool in mathematics, and they help us simplify complex expressions and solve equations.

Evaluating Exponential Expressions

To evaluate an exponential expression, we need to follow the order of operations (PEMDAS):

  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 $10^0 + 10^1 + 10^2$

Now that we have a basic understanding of exponents and how to evaluate them, let's apply this knowledge to the expression $10^0 + 10^1 + 10^2$.

Step 1: Evaluate the Exponents

Using the properties of exponents, we know that:

  • 10^0 = 1$ (since any number raised to the power of 0 is 1)

  • 10^1 = 10$ (since any number raised to the power of 1 is itself)

  • 10^2 = 100$ (since 10 squared is 100)

Step 2: Add the Results

Now that we have evaluated the exponents, we can add the results:

100+101+102=1+10+100=11110^0 + 10^1 + 10^2 = 1 + 10 + 100 = 111

Conclusion

In conclusion, the correct answer to the expression $10^0 + 10^1 + 10^2$ is C. 111. We evaluated the exponents using the properties of exponents and then added the results to obtain the final answer.

Why is this Important?

Understanding exponential expressions and how to evaluate them is crucial in mathematics. It helps us solve equations, simplify complex expressions, and make predictions about real-world phenomena. In this article, we applied the concept of exponents to a simple expression and obtained a clear and concise answer.

Common Mistakes to Avoid

When evaluating exponential expressions, it's essential to follow the order of operations (PEMDAS) and to use the properties of exponents correctly. Some common mistakes to avoid include:

  • Not following the order of operations (PEMDAS)
  • Not using the properties of exponents correctly
  • Not evaluating the exponents before adding or subtracting the results

Real-World Applications

Exponential expressions have numerous real-world applications, including:

  • Finance: Exponential expressions are used to calculate compound interest and investment returns.
  • Science: Exponential expressions are used to model population growth, chemical reactions, and other phenomena.
  • Engineering: Exponential expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.

Conclusion

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about exponential expressions and evaluating $10^0 + 10^1 + 10^2$.

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 evaluating an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • 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: How do I evaluate an exponential expression?

A: To evaluate an exponential expression, you need to follow the order of operations (PEMDAS). Here's a step-by-step guide:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the value of $10^0$?

A: The value of $10^0$ is 1. This is because any number raised to the power of 0 is 1.

Q: What is the value of $10^1$?

A: The value of $10^1$ is 10. This is because any number raised to the power of 1 is itself.

Q: What is the value of $10^2$?

A: The value of $10^2$ is 100. This is because 10 squared is 100.

Q: How do I add the results of $10^0 + 10^1 + 10^2$?

A: To add the results of $10^0 + 10^1 + 10^2$, you need to follow the order of operations (PEMDAS). Here's a step-by-step guide:

  1. Evaluate the exponents: $10^0 = 1$, $10^1 = 10$, and $10^2 = 100$.
  2. Add the results: $1 + 10 + 100 = 111$.

Q: What is the correct answer to the expression $10^0 + 10^1 + 10^2$?

A: The correct answer to the expression $10^0 + 10^1 + 10^2$ is C. 111.

Q: Why is it essential to follow the order of operations (PEMDAS)?

A: It's essential to follow the order of operations (PEMDAS) because it ensures that we evaluate expressions correctly and avoid errors. By following the order of operations, we can ensure that we get the correct answer to an expression.

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

A: Exponential expressions have numerous real-world applications, including:

  • Finance: Exponential expressions are used to calculate compound interest and investment returns.
  • Science: Exponential expressions are used to model population growth, chemical reactions, and other phenomena.
  • Engineering: Exponential expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.

Conclusion

In conclusion, understanding exponential expressions and how to evaluate them is a fundamental concept in mathematics. By following the order of operations (PEMDAS) and using the properties of exponents correctly, we can solve equations, simplify complex expressions, and make predictions about real-world phenomena. In this article, we addressed some of the most frequently asked questions about exponential expressions and evaluating $10^0 + 10^1 + 10^2$.