How would you equate equations with exponents to zero?

I am not entirely sure what kind of equation you want to solve. Anyway, if an expression has an exponent of zero, the entire expression is usually equal to 1 (unless you raise zero to the power zero; that's undefined). Perhaps that can help you simplify the expression. For example: if you have an equation such as
(x+y+z)0 + 5x + 3 = 10
The entire left expression, (x+y+z)0 can be replaced with 1, thus simplifying the equation.
I am not entirely sure what kind of equation you want to solve. Anyway, if an expression has an exponent of zero, the entire expression is usually equal to 1 (unless you raise zero to the power zero; that's undefined). Perhaps that can help you simplify the expression. For example: if you have an equation such as
(x+y+z)0 + 5x + 3 = 10
The entire left expression, (x+y+z)0 can be replaced with 1, thus simplifying the equation.