We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:
(1/32)^x = (2^3)^3-x
Simplifying the right side:
(1/32)^x = 2^(9-3x)
We can write both sides using a common base, say 2:
2^(-5x) = 2^(9-3x)
Now we equate the exponents and solve for x:
-5x = 9 - 3x
-2x = 9
x = -4.5
Therefore, the solution to the equation is x = -4.5.