Evaluate. Write Your Answer As A Fraction Or Whole Number Without Exponents.${ 1^{-2} = \square }$
Understanding the Concept of Negative Exponents
When dealing with negative exponents, it's essential to understand the concept of reciprocals and how they relate to positive exponents. A negative exponent indicates that the reciprocal of the base should be taken, and the exponent should be made positive. In other words, a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent.
Evaluating the Expression 1^(-2)
To evaluate the expression 1^(-2), we need to apply the concept of negative exponents. Since the base is 1, we know that any power of 1 will result in 1. However, the negative exponent indicates that we need to take the reciprocal of 1.
The Reciprocal of 1
The reciprocal of 1 is simply 1 itself. This is because the reciprocal of a number is obtained by dividing 1 by that number. In this case, the reciprocal of 1 is 1/1, which simplifies to 1.
Applying the Concept of Negative Exponents
Now that we understand the concept of negative exponents and the reciprocal of 1, we can apply this knowledge to evaluate the expression 1^(-2). Since the base is 1, we know that any power of 1 will result in 1. However, the negative exponent indicates that we need to take the reciprocal of 1.
Simplifying the Expression
Using the concept of negative exponents, we can simplify the expression 1^(-2) as follows:
1^(-2) = 1 / (1^2) = 1 / 1 = 1
Conclusion
In conclusion, the expression 1^(-2) can be evaluated as 1. This is because the base is 1, and the negative exponent indicates that we need to take the reciprocal of 1. The reciprocal of 1 is simply 1 itself, which simplifies the expression to 1.
Frequently Asked Questions
- What is the value of 1^(-2)?
- How do you evaluate an expression with a negative exponent?
- What is the reciprocal of 1?
Answer
- The value of 1^(-2) is 1.
- To evaluate an expression with a negative exponent, you need to take the reciprocal of the base and make the exponent positive.
- The reciprocal of 1 is 1 itself.
Final Answer
The final answer is .
Introduction
Evaluating expressions with negative exponents can be a challenging task, especially for those who are new to algebra. However, with a clear understanding of the concept of negative exponents and how to apply it, you can easily evaluate expressions with negative exponents. In this article, we will provide a comprehensive guide to evaluating expressions with negative exponents, including a Q&A section to help you understand the concept better.
Understanding Negative Exponents
A negative exponent indicates that the reciprocal of the base should be taken, and the exponent should be made positive. In other words, a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent.
Evaluating Expressions with Negative Exponents
To evaluate an expression with a negative exponent, you need to follow these steps:
- Identify the base and the exponent.
- Take the reciprocal of the base.
- Make the exponent positive.
- Evaluate the expression.
Q&A Section
Q: What is the value of 2^(-3)?
A: To evaluate the expression 2^(-3), we need to take the reciprocal of 2 and make the exponent positive. The reciprocal of 2 is 1/2, and the positive exponent is 3. Therefore, the value of 2^(-3) is (1/2)^3 = 1/8.
Q: How do you evaluate the expression x^(-2)?
A: To evaluate the expression x^(-2), we need to take the reciprocal of x and make the exponent positive. The reciprocal of x is 1/x, and the positive exponent is 2. Therefore, the value of x^(-2) is (1/x)^2 = 1/x^2.
Q: What is the value of (1/2)^(-2)?
A: To evaluate the expression (1/2)^(-2), we need to take the reciprocal of 1/2 and make the exponent positive. The reciprocal of 1/2 is 2, and the positive exponent is 2. Therefore, the value of (1/2)^(-2) is 2^2 = 4.
Q: How do you evaluate the expression (x2)(-3)?
A: To evaluate the expression (x2)(-3), we need to take the reciprocal of x^2 and make the exponent positive. The reciprocal of x^2 is 1/x^2, and the positive exponent is 3. Therefore, the value of (x2)(-3) is (1/x2)3 = 1/x^6.
Q: What is the value of (23)(-2)?
A: To evaluate the expression (23)(-2), we need to take the reciprocal of 2^3 and make the exponent positive. The reciprocal of 2^3 is 1/2^3, and the positive exponent is 2. Therefore, the value of (23)(-2) is (1/23)2 = 1/2^6 = 1/64.
Conclusion
Evaluating expressions with negative exponents can be a challenging task, but with a clear understanding of the concept and how to apply it, you can easily evaluate expressions with negative exponents. By following the steps outlined in this article and using the Q&A section to help you understand the concept better, you can become proficient in evaluating expressions with negative exponents.
Final Answer
The final answer is .