Final answer:
The expression (5^-2)^5 * 5^4 is equivalent to 1/5^14.
Step-by-step explanation:
To simplify the expression (5-2)5 * 54, we need to apply the power rule, which states that when you raise an exponent to another exponent, you multiply the exponents. We first calculate (5-2)5 as (1/52)5 = 1/510. Then we multiply this result by 54 to get (1/510) * 54. To multiply these expressions, we add the exponents, so we have 1/510+4 = 1/514. Therefore, the expression is equivalent to option C, 1/514.