How to find the value of 5 variables

Question

I have an equation: $$O^R-C+K^Y=ROCKY$$ All of the variables are whole numbers from $0$ to $9$ inclusive. There cannot be any duplicate numbers. I need to find the value of all of the variables.

Answer 1

A quick brute-force Python script reveals $$9^5-2+6^3=59263$$

Answer 2

Let one of the numbers be 0. Then the RHS becomes zero and we can look for 4 other numbers that together satisfy: $$O^R+K^Y=C$$ And this is quite doable by hand. Starting with the most trivial solutions where one of the remaining numbers is a 1: $$k^0+n^1=(n+1), n\in\{2, ..., 8\}$$ $$k^0+1^n=2$$

Any integer power greater than $2^3$ and $3^2$ will exceed the allowed range for $C$, but we can still toy around with these two: $$k^0+2^3=9, k\in\{1,4,5,6,7,8\}$$ $$0^k+2^3=8, k\in\{1,4,5,6,7,9\}$$ $$0^k+3^2=9, k\in\{1,4,5,6,7,8\}$$