To determine how to represent the product [tex]\(5 \cdot 5 \cdot 5 \cdot 5\)[/tex] in exponential notation, let's break it down step-by-step.
1. Exponential notation is a way of expressing repeated multiplication of the same number. For example, [tex]\(a^b\)[/tex] means [tex]\(a\)[/tex] (the base) is multiplied by itself [tex]\(b\)[/tex] (the exponent) number of times.
2. In the given expression [tex]\(5 \cdot 5 \cdot 5 \cdot 5\)[/tex], the number 5 is being multiplied by itself 4 times.
3. Therefore, this repeated multiplication can be written in exponential notation as [tex]\(5^4\)[/tex], where 5 is the base, and 4 is the exponent indicating how many times 5 is multiplied by itself.
Reviewing the options given:
- 4: This is just a number and does not represent the repeated multiplication of 5.
- [tex]\(4 \cdot 5\)[/tex]: This indicates a simple multiplication of 4 and 5, which equals 20.
- [tex]\(4^5\)[/tex]: This represents 4 multiplied by itself 5 times, which is not what the original expression shows.
- [tex]\(5^4\)[/tex]: This correctly represents [tex]\(5 \cdot 5 \cdot 5 \cdot 5\)[/tex].
Thus, the correct exponential notation for [tex]\(5 \cdot 5 \cdot 5 \cdot 5\)[/tex] is [tex]\(\boxed{5^4}\)[/tex].
