Which Expression Is { M \cdot M \cdot M \cdot M \cdot M $}$ Rewritten In Exponential Form?A. { M^5 $}$ B. { 5m $}$ C. { 5^m $}$ D. { M+5 $}$
Introduction
In mathematics, expressions can be rewritten in various forms to simplify or clarify their meaning. One common form is exponential notation, which represents repeated multiplication as a single operation. In this article, we will explore how to rewrite an expression in exponential form and apply this concept to a specific problem.
What is Exponential Form?
Exponential form is a way of writing repeated multiplication as a single operation. It is denoted by a base number raised to a power, such as 2^3 or 5^4. The base number is the number being multiplied, and the exponent is the number of times the base is multiplied by itself.
How to Rewrite Expressions in Exponential Form
To rewrite an expression in exponential form, we need to identify the base number and the exponent. The base number is the number being multiplied, and the exponent is the number of times the base is multiplied by itself.
For example, consider the expression 2 × 2 × 2 × 2 × 2. We can rewrite this expression in exponential form as 2^5, where 2 is the base number and 5 is the exponent.
The Problem: Rewriting { m \cdot m \cdot m \cdot m \cdot m $}$ in Exponential Form
Now, let's apply this concept to the problem at hand. We are given the expression { m \cdot m \cdot m \cdot m \cdot m $}$ and asked to rewrite it in exponential form.
To do this, we need to identify the base number and the exponent. In this case, the base number is m, and the exponent is 5, since the expression is repeated 5 times.
Therefore, the correct answer is { m^5 $}$.
Why is { m^5 $}$ the Correct Answer?
The correct answer is { m^5 $}$ because it accurately represents the repeated multiplication of m by itself 5 times. The base number m is raised to the power of 5, which means that m is multiplied by itself 5 times.
Why are the Other Options Incorrect?
Let's examine the other options to see why they are incorrect.
Option B, { 5m $}$, is incorrect because it does not accurately represent the repeated multiplication of m by itself 5 times. Instead, it represents the product of 5 and m.
Option C, { 5^m $}$, is incorrect because it represents the exponentiation of 5 to the power of m, rather than the repeated multiplication of m by itself 5 times.
Option D, { m+5 $}$, is incorrect because it represents the sum of m and 5, rather than the repeated multiplication of m by itself 5 times.
Conclusion
In conclusion, the correct answer to the problem is { m^5 $}$, which accurately represents the repeated multiplication of m by itself 5 times. This example illustrates the importance of understanding exponential form and how to rewrite expressions in this form.
Common Mistakes to Avoid
When rewriting expressions in exponential form, it's essential to avoid common mistakes. Here are a few to watch out for:
- Misidentifying the base number: Make sure to identify the base number correctly, as this will affect the exponent.
- Miscounting the exponent: Double-check the exponent to ensure it accurately represents the number of times the base is multiplied by itself.
- Confusing exponential form with other forms: Be careful not to confuse exponential form with other forms, such as multiplication or addition.
Practice Problems
To reinforce your understanding of rewriting expressions in exponential form, try the following practice problems:
- Rewrite the expression 3 × 3 × 3 × 3 × 3 in exponential form.
- Rewrite the expression 2 × 2 × 2 × 2 × 2 × 2 in exponential form.
- Rewrite the expression 4 × 4 × 4 × 4 in exponential form.
Answer Key
- 3^5
- 2^6
- 4^4
Final Thoughts
Introduction
In our previous article, we explored the concept of rewriting expressions in exponential form. We discussed how to identify the base number and the exponent, and how to apply this concept to a specific problem. In this article, we will continue to build on this concept by answering some frequently asked questions about exponential form and rewriting expressions.
Q: What is the difference between exponential form and other forms of writing expressions?
A: Exponential form is a way of writing repeated multiplication as a single operation. It is denoted by a base number raised to a power, such as 2^3 or 5^4. Other forms of writing expressions, such as multiplication or addition, do not represent repeated multiplication in the same way.
Q: How do I know when to use exponential form?
A: You should use exponential form when you are writing an expression that involves repeated multiplication. For example, if you have the expression 2 × 2 × 2 × 2 × 2, you should rewrite it in exponential form as 2^5.
Q: What is the base number in an exponential expression?
A: The base number is the number being multiplied. In the expression 2^5, the base number is 2.
Q: What is the exponent in an exponential expression?
A: The exponent is the number of times the base is multiplied by itself. In the expression 2^5, the exponent is 5.
Q: Can I have a negative exponent?
A: Yes, you can have a negative exponent. A negative exponent represents the reciprocal of the base raised to the positive exponent. For example, 2^(-3) is equal to 1/2^3.
Q: Can I have a fractional exponent?
A: Yes, you can have a fractional exponent. A fractional exponent represents the base raised to the power of a fraction. For example, 2^(1/2) is equal to the square root of 2.
Q: How do I simplify an exponential expression?
A: To simplify an exponential expression, you can use the following rules:
- Product of powers: When you multiply two exponential expressions with the same base, you can add the exponents. For example, 2^3 × 2^4 = 2^(3+4) = 2^7.
- Power of a power: When you raise an exponential expression to a power, you can multiply the exponents. For example, (23)4 = 2^(3×4) = 2^12.
- Zero exponent: Any number raised to the power of 0 is equal to 1. For example, 2^0 = 1.
Q: How do I rewrite an expression in exponential form?
A: To rewrite an expression in exponential form, you can follow these steps:
- Identify the base number: Determine the number being multiplied.
- Identify the exponent: Determine the number of times the base is multiplied by itself.
- Write the expression in exponential form: Write the base number raised to the power of the exponent.
Q: What are some common mistakes to avoid when rewriting expressions in exponential form?
A: Some common mistakes to avoid when rewriting expressions in exponential form include:
- Misidentifying the base number: Make sure to identify the base number correctly, as this will affect the exponent.
- Miscounting the exponent: Double-check the exponent to ensure it accurately represents the number of times the base is multiplied by itself.
- Confusing exponential form with other forms: Be careful not to confuse exponential form with other forms, such as multiplication or addition.
Conclusion
In conclusion, rewriting expressions in exponential form is a fundamental concept in mathematics that can help simplify complex expressions and make them easier to understand. By following the steps outlined in this article and practicing with sample problems, you can become more confident in your ability to rewrite expressions in exponential form.