The basic rule in adding and subtracting variables with exponents is they must be like terms. Like terms consist of the same variable or set of variables raised to the same power. The numerical coefficients of these terms may vary, and these are the elements that undergo the addition or subtraction process. The algebraic expressions 2x, 7x and x are like terms, as well as, 4ab^2 and 21ab^2.

To simplify an algebraic expression, look for like terms. If two terms have the same variables but have different exponents, they cannot be combined. In the expression 8x - 10y + 3x, the like terms are 8x and 3x. The sum of their numerical coefficients must be attached to the common variable and corresponding exponent. Thus, the simplified version of the expression is 11x – 10y. The two remaining terms cannot be combined because they are not like terms.

In the example 6x^2y^2z + xyz - x^2y^2z, the like terms are 6x^2y^2z and x^2y^2z. Subtraction is the operation necessary to combine these two terms. The difference is 5x^2y^2z. Therefore, 5x^2y^2z + xyz is the given expression in its simplified form. The variables and exponents in the like terms remain unaltered in the final equation.