How do you multiply a base of 34 and a exponent of 0?

Actually, a base and exponent are not multiplied together. Rather, the exponent indicates the "power" of the base number, the number of times the base is to be multiplied by itself. For example the expression 23, where the base is 2 and the exponent is 3, represents the product of 3 2s; that is, 2 x 2 x 2, equaling 8. Powers of zero are a special case. By convention, and to support exponent operations, any number (excepting zero) to the power of zero equals one. Therefore the number with a base of 34 and exponent of 0 is written as 340, and 340 = 1.