Answer:
C.
Explanation:
1. Simplify the bases: Rewrite 125 as 5^3 and (1/25) as (1/5)^2.
(5^3)^(x-2) = ((1/5)^2)^(3x)
2. Apply the power of a power rule: Multiply the exponents when raising a power to another power.
5^(3(x-2)) = (1/5)^(2(3x))
3. Simplify the exponents: Distribute the exponents.
5^(3x-6) = (1/5)^(6x)
4. Convert the bases to a common base: Both sides of the equation have bases of 5, so we can rewrite (1/5) as 5^(-1).
5^(3x-6) = 5^(-6x)
5. Set the exponents equal to each other: Since the bases are the same, the exponents must be equal.
3x - 6 = -6x
6. Solve for x: Combine like terms and isolate x.
3x + 6x = 6
9x = 6
x = 6/9
x = 2/3
Therefore, the value of x that satisfies the equation is 2/3.