Thank you for the opportunity to help you with your question!

To solve this problem, you need to make sure the bases (1/2 and 8) are the same. You can change the base to '2' for each of them, then set the exponents equal to each other to solve for x:

(1/2)^3x = 8^(x-2)

2^(-1*3x) = 2^(3*(x-2)) Rewrite (1/2) as 2^-1 and rewrite 8 as 2^3. Those exponents are multiplied by the exponents that are already there ( 3x and x-2)

-1*3x = 3*(x-2) Since you have the same bases, you can set the exponents equal to each other.

-3x = 3x - 6

6x = 6

x = 1

Please let me know if you need any clarification. I'm always happy to answer your questions.