Final answer:
The expression (2⁵)/(6⁵) is equivalent to 3⁻⁵. We use the rule for dividing powers with the same base to subtract the exponents and get 2⁰/6⁰, which simplifies to 1 and can be represented as (1/3)⁵.
Step-by-step explanation:
When determining which expressions are equivalent to (2⁵)/(6⁵), we apply the rule for dividing powers with the same base. In this case, we subtract the exponents: 5 - 5, which results in 2⁰/6⁰. Since any non-zero number raised to the power of 0 is 1, both the numerator and denominator become 1, leaving us with 1/1 or simply 1.
This expression can be written as (1/3)⁵, indicating that (B) 3⁵ is one of the correct answers because 3 to the power of -5 is the reciprocal of 3 to the power of 5.
None of the other choices, (A) 1/3 or (C) (-4)⁵, are equivalent because they do not represent the original expression correctly once the rules of exponents have been applied.