$a^{x}+b^{y}=c^{z}$
Final Answer: \(\boxed{\text{There is no unique solution without specific values for the variables.}}\)
Step 1 :Given the equation: \(a^{x}+b^{y}=c^{z}\)
Step 2 :Since there are multiple variables and no specific values given, we cannot find a unique solution.
Step 3 :However, we can create a Python function to check if the equation holds true for given values of a, b, c, x, y, and z.
Step 4 :Final Answer: \(\boxed{\text{There is no unique solution without specific values for the variables.}}\)