Kenisha Evaluated The Power As Shown:$\left(\frac{3}{2}\right)^3 = \frac{(3)(3)(3)}{2} = \frac{27}{2}$Did Kenisha Correctly Evaluate The Power? If Not, Why Not?A. Yes, She Evaluated The Power Correctly. B. No, She Should Have Used Only 2

Understanding Exponents

Exponents are a fundamental concept in mathematics that help us simplify complex expressions and solve equations. In this article, we will delve into the world of exponents and explore how to evaluate them correctly.

What is an Exponent?

An exponent is a small number that is placed above and to the right of a base number. It tells us how many times to multiply the base number by itself. For example, in the expression $2^3$, the exponent 3 tells us to multiply 2 by itself 3 times: $2^3 = 2 \times 2 \times 2 = 8$.

Evaluating Exponents: A Step-by-Step Guide

To evaluate an exponent, we need to follow a simple step-by-step process:

1. Identify the base number: The base number is the number that is being multiplied by itself. In the expression $2^3$, the base number is 2.
2. Identify the exponent: The exponent is the small number that is placed above and to the right of the base number. In the expression $2^3$, the exponent is 3.
3. Multiply the base number by itself: We need to multiply the base number by itself as many times as indicated by the exponent. In the expression $2^3$, we need to multiply 2 by itself 3 times: $2 \times 2 \times 2 = 8$.
4. Write the result: The result of multiplying the base number by itself is the final answer. In the expression $2^3$, the final answer is 8.

Evaluating the Power: A Real-World Example

Let's consider the example given by Kenisha: $\left(\frac{3}{2}\right)^3 = \frac{(3)(3)(3)}{2} = \frac{27}{2}$. To evaluate this expression, we need to follow the step-by-step process outlined above.

1. Identify the base number: The base number is $\frac{3}{2}$.
2. Identify the exponent: The exponent is 3.
3. Multiply the base number by itself: We need to multiply $\frac{3}{2}$ by itself 3 times: $\left(\frac{3}{2}\right)^3 = \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right)$.
4. Write the result: The result of multiplying $\frac{3}{2}$ by itself 3 times is $\frac{27}{8}$, not $\frac{27}{2}$.

Conclusion

In conclusion, Kenisha did not evaluate the power correctly. She should have used the correct exponent rule to evaluate the expression: $\left(\frac{3}{2}\right)^3 = \frac{27}{8}$, not $\frac{27}{2}$.

Common Mistakes to Avoid

When evaluating exponents, it's essential to avoid common mistakes such as:

• Not following the order of operations: When evaluating an expression with multiple operations, we need to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Not using the correct exponent rule: The exponent rule states that when we raise a fraction to a power, we need to raise both the numerator and the denominator to that power.
• Not simplifying the expression: We need to simplify the expression by combining like terms and canceling out any common factors.

Tips and Tricks

Here are some tips and tricks to help you evaluate exponents like a pro:

• Use the exponent rule: When evaluating an expression with a fraction, use the exponent rule to raise both the numerator and the denominator to the power.
• Simplify the expression: Simplify the expression by combining like terms and canceling out any common factors.
• Use a calculator: If you're struggling to evaluate an expression, use a calculator to check your work.

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about evaluating exponents.

Q: What is an exponent?

A: An exponent is a small number that is placed above and to the right of a base number. It tells us how many times to multiply the base number by itself.

Q: How do I evaluate an exponent?

A: To evaluate an exponent, we need to follow a simple step-by-step process:

1. Identify the base number: The base number is the number that is being multiplied by itself.
2. Identify the exponent: The exponent is the small number that is placed above and to the right of the base number.
3. Multiply the base number by itself: We need to multiply the base number by itself as many times as indicated by the exponent.
4. Write the result: The result of multiplying the base number by itself is the final answer.

Q: What is the order of operations when evaluating exponents?

A: When evaluating an expression with multiple operations, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponents 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.

Q: How do I handle negative exponents?

A: When we have a negative exponent, we need to take the reciprocal of the base number and change the sign of the exponent. For example, $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$.

Q: How do I handle fractional exponents?

A: When we have a fractional exponent, we need to take the root of the base number and raise it to the power of the numerator. For example, $\sqrt[3]{2^2} = (2^2)^{1/3} = 2^{2/3}$.

Q: Can I simplify an expression with an exponent?

A: Yes, we can simplify an expression with an exponent by combining like terms and canceling out any common factors. For example, $2^3 \times 2^2 = 2^{3+2} = 2^5 = 32$.

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

A: When we have an expression with multiple exponents, we need to follow the order of operations and evaluate each exponent separately. For example, $(2^3)^2 = 2^{3 \times 2} = 2^6 = 64$.

Q: Can I use a calculator to evaluate an exponent?

A: Yes, we can use a calculator to evaluate an exponent. However, it's always a good idea to check your work by hand to make sure you understand the concept.

Conclusion

In conclusion, evaluating exponents is a fundamental concept in mathematics that requires attention to detail and a step-by-step approach. By following the step-by-step process outlined above and avoiding common mistakes, you can evaluate exponents like a pro. Remember to use the exponent rule, simplify the expression, and use a calculator if needed. With practice and patience, you'll become a master of evaluating exponents in no time!

Common Mistakes to Avoid

When evaluating exponents, it's essential to avoid common mistakes such as:

• Not following the order of operations: When evaluating an expression with multiple operations, we need to follow the order of operations (PEMDAS).
• Not using the correct exponent rule: The exponent rule states that when we raise a fraction to a power, we need to raise both the numerator and the denominator to that power.
• Not simplifying the expression: We need to simplify the expression by combining like terms and canceling out any common factors.

Tips and Tricks

Here are some tips and tricks to help you evaluate exponents like a pro:

• Use the exponent rule: When evaluating an expression with a fraction, use the exponent rule to raise both the numerator and the denominator to the power.
• Simplify the expression: Simplify the expression by combining like terms and canceling out any common factors.
• Use a calculator: If you're struggling to evaluate an expression, use a calculator to check your work.

Conclusion

In conclusion, evaluating exponents is a fundamental concept in mathematics that requires attention to detail and a step-by-step approach. By following the step-by-step process outlined above and avoiding common mistakes, you can evaluate exponents like a pro. Remember to use the exponent rule, simplify the expression, and use a calculator if needed. With practice and patience, you'll become a master of evaluating exponents in no time!