Certainly! Let's explore how a prime number, such as 7, can be written in exponential form.
### Understanding Prime Numbers
Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. Prime numbers have no other divisors besides 1 and the number itself.
### Writing Numbers in Exponential Form
Writing a number in exponential form typically involves expressing it as a product of repeated multiplicative factors of a base number raised to an exponent.
For example:
- \( 2^3 = 2 \times 2 \times 2 = 8 \)
- \( 5^2 = 5 \times 5 = 25 \)
### Applying this to Prime Numbers
To express a prime number in exponential form, we need to find a base and an exponent such that when the base is raised to the exponent, it equals the prime number.
In the case of the prime number 7:
- Since 7 is already a prime number, it doesn't need any more factors to express it in exponential form.
- We can consider 7 as being \( 7 \times 1 \).
- Consequently, the simplest and most direct exponential form of 7 is \( 7^1 \).
So, for the prime number 7:
- The base is 7.
- The exponent is 1.
- The exponential form is \( 7^1 \).
Thus, we can perfectly express the prime number 7 in exponential form as \( 7^1 \).
### Conclusion
Prime numbers can indeed be written in exponential form by raising them to the power of 1. For the prime number 7, it can be written in exponential form as \( 7^1 \):
\( \text{Base} = 7 \)
\( \text{Exponent} = 1 \)
\( 7^1 = 7 \)
Therefore, the exponential form of the prime number 7 is [tex]\( 7^1 \)[/tex].
