Rewriting Exponents in Expanded Form

Oct 13, 2025 by miodeya.com 132 views

Introduction

In mathematics, exponents are a fundamental concept used to represent repeated multiplication of a number. When we see an expression like $$7^{11}$$, it means that the number 7 is multiplied by itself 11 times. However, when we rewrite this expression in expanded form, we get a series of terms that are multiplied together. In this article, we will explore how to rewrite exponents in expanded form and determine the number of terms that will be multiplied in the rewritten expression.

Understanding Exponents

Before we dive into rewriting exponents in expanded form, let's take a moment to understand what exponents represent. An exponent is a small number that is placed above and to the right of a base number. The exponent tells us how many times the base number should be multiplied by itself. For example, in the expression $$7^{11}$$, the base number is 7 and the exponent is 11. This means that 7 should be multiplied by itself 11 times.

Rewriting Exponents in Expanded Form

Now that we understand what exponents represent, let's explore how to rewrite them in expanded form. When we rewrite an exponent in expanded form, we get a series of terms that are multiplied together. To rewrite an exponent in expanded form, we can use the following formula:

a^{n} = a \cdot a \cdot a \cdot ... \cdot a

where $a$ is the base number and $n$ is the exponent.

For example, let's rewrite the expression $$7^{11}$$ in expanded form using the formula above:

7^{11} = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7

As we can see, the rewritten expression consists of 11 terms that are multiplied together.

Determining the Number of Terms

Now that we have rewritten the expression $$7^{11}$$ in expanded form, let's determine the number of terms that will be multiplied in the rewritten expression. As we can see from the rewritten expression above, there are 11 terms that are multiplied together. Therefore, the number of terms that will be multiplied in the rewritten expression is 11.

Conclusion

In conclusion, rewriting exponents in expanded form is a useful technique that allows us to represent repeated multiplication of a number in a more explicit way. By using the formula $$a^{n} = a \cdot a \cdot a \cdot ... \cdot a$$, we can rewrite exponents in expanded form and determine the number of terms that will be multiplied in the rewritten expression. In the case of the expression $$7^{11}$$, we found that there are 11 terms that will be multiplied in the rewritten expression.

Answer

Based on our analysis, the correct answer is:

C. 11

This is because there are 11 terms that will be multiplied in the rewritten expression $$7^{11}$$.

Additional Examples

To further illustrate the concept of rewriting exponents in expanded form, let's consider a few additional examples:

$2^{5} = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$
$3^{4} = 3 \cdot 3 \cdot 3 \cdot 3$
$4^{3} = 4 \cdot 4 \cdot 4$

In each of these examples, we can see that the rewritten expression consists of the same number of terms as the exponent. This is a general rule that applies to all exponents: the number of terms in the rewritten expression is equal to the exponent.

Final Thoughts

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about rewriting exponents in expanded form.

Q: What is an exponent?

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

Q: How do I rewrite an exponent in expanded form?

A: To rewrite an exponent in expanded form, you can use the formula:

a^{n} = a \cdot a \cdot a \cdot ... \cdot a

where $a$ is the base number and $n$ is the exponent.

Q: What is the number of terms in the rewritten expression?

A: The number of terms in the rewritten expression is equal to the exponent.

Q: Can you give me an example of rewriting an exponent in expanded form?

A: Let's consider the expression $$7^{11}$$. To rewrite this expression in expanded form, we can use the formula above:

7^{11} = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7

As we can see, the rewritten expression consists of 11 terms that are multiplied together.

Q: How do I determine the number of terms in the rewritten expression?

A: To determine the number of terms in the rewritten expression, you can simply count the number of terms in the expanded form.

Q: Can you give me some additional examples of rewriting exponents in expanded form?

A: Here are a few additional examples:

$2^{5} = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$
$3^{4} = 3 \cdot 3 \cdot 3 \cdot 3$
$4^{3} = 4 \cdot 4 \cdot 4$

In each of these examples, we can see that the rewritten expression consists of the same number of terms as the exponent.

Q: What is the importance of rewriting exponents in expanded form?

A: Rewriting exponents in expanded form is an important technique in mathematics because it allows us to represent repeated multiplication of a number in a more explicit way. This can be useful in a variety of mathematical contexts, such as algebra and calculus.

Q: Can you give me some real-world examples of rewriting exponents in expanded form?

A: Here are a few real-world examples:

In finance, exponents are used to calculate compound interest. For example, if you invest $100 at a 5% annual interest rate, the amount of money you will have after 5 years can be calculated using the formula $$100 \cdot 1.05^{5}$$.
In science, exponents are used to calculate the growth of populations. For example, if a population of bacteria doubles every hour, the number of bacteria after 5 hours can be calculated using the formula $$100 \cdot 2^{5}$$.

Conclusion

In conclusion, rewriting exponents in expanded form is a powerful technique that allows us to represent repeated multiplication of a number in a more explicit way. By using the formula $$a^{n} = a \cdot a \cdot a \cdot ... \cdot a$$, we can rewrite exponents in expanded form and determine the number of terms that will be multiplied in the rewritten expression. We hope that this article has provided a clear and concise explanation of this concept and has helped to illustrate its importance in mathematics.