Final answer:
To rewrite the expression involving powers of 5, we add the exponents (4, -8, and 1) to get 5^(-3), thus using the base only once.
Step-by-step explanation:
To rewrite the expression 5^(4)*5^(-8)*5 using the base only once, we apply the rules for multiplying powers with the same base. According to the laws of exponents, when multiplying powers with the same base, we add the exponents. Thus, the given expression simplifies as follows:
5^(4 + (-8) + 1) = 5^(-3).
Therefore, by applying the rule of adding exponents, we can express the original multiplication of powers of 5 using the base only once.