We are asked to solve the equation $125^{2-3x} = 5^{-3}$ for $x$.

1. Problem Description

We are asked to solve the equation $125^{2-3x} = 5^{-3}$ for $x$.

2. Solution Steps

First, we can rewrite 125 as $5^3$. So, the equation becomes:

$(5^3)^{2-3x} = 5^{-3}$

Using the power of a power rule, $(a^m)^n = a^{mn}$, we get:

$5^{3(2-3x)} = 5^{-3}$

Since the bases are equal, we can set the exponents equal to each other:

$3(2-3x) = -3$

Distribute the 3 on the left side:

$6 - 9x = -3$

Subtract 6 from both sides:

$-9x = -3 - 6$

$-9x = -9$

Divide both sides by -9:

$x = \frac{-9}{-9}$

$x = 1$

3. Final Answer

The solution is $x = 1$.