Answer :

To express 3125 in exponential form with base 5, we need to find a number such that [tex]\( 5 \)[/tex] raised to the power of that number equals 3125. Here's a step-by-step solution to achieve that:

1. Understand the problem: We need to express 3125 as [tex]\( 5^x \)[/tex], where [tex]\( x \)[/tex] is an exponent. Specifically, we are searching for the exponent [tex]\( x \)[/tex] that satisfies the equation.

2. Start with the base number: The base given in the problem is 5. We need to see how many times we can multiply 5 by itself to get 3125.

3. Perform exponentiation until you reach 3125:

- [tex]\( 5^1 = 5 \)[/tex]
- [tex]\( 5^2 = 25 \)[/tex]
- [tex]\( 5^3 = 125 \)[/tex]
- [tex]\( 5^4 = 625 \)[/tex]
- [tex]\( 5^5 = 3125 \)[/tex]

4. Identify the exponent: By listing these calculations, we see that [tex]\( 5^5 \)[/tex] equals 3125.

Therefore, 3125 in exponential form with base 5 is:

[tex]\[ 5^5 \][/tex]

So, the exponential form of 3125 with base 5 is [tex]\( 5^5 \)[/tex].

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