Certainly! Let's express the number [tex]\( 15625 \)[/tex] as a product of its prime factors in a detailed, step-by-step manner.
First, recognize we are given that [tex]\( 15625 \)[/tex] can be factored into prime factors. To start, we need to know which prime number can perfectly divide [tex]\( 15625 \)[/tex] and how many times it can divide completely.
We find that the prime number involved here is [tex]\( 5 \)[/tex]. Let's confirm this through the information provided:
1. The number [tex]\( 15625 \)[/tex] can be factored as:
[tex]\[ 15625 = 5^6 \][/tex]
This indicates that the prime factor is 5, and it is raised to the power of 6.
Thus, expressing [tex]\( 15625 \)[/tex] as the product of prime factors, we have:
[tex]\[ 15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \][/tex]
or more succinctly:
[tex]\[ 15625 = 5^6 \][/tex]
In conclusion, [tex]\( 15625 \)[/tex] is expressed as the product of its prime factor [tex]\( 5 \)[/tex], raised to the sixth power, i.e., [tex]\( 5^6 \)[/tex].
