Final answer:
To find the number of different pizzas Maria's trattoria can make with seven available toppings, we use the formula 2^n for combinations, resulting in 2^7 = 128 different pizzas, including the option of a plain cheese pizza.
Step-by-step explanation:
The question involves determining the number of different pizzas that can be made given a set of toppings on a plain cheese base. Maria's trattoria offers seven toppings: onions, ham, mushrooms, green peppers, black olives, anchovies, and pepperoni. To solve this problem, we recognize that each topping can either be on the pizza or not, which is a binary choice. Hence, for each of the seven toppings, there are 2 choices - to include or exclude.
To calculate the total number of different pizza combinations, we raise the number of choices for each topping to the power of the number of toppings. The formula for this calculation is 2^n, where n is the number of toppings. In this case, n=7, so the calculation is 2^7.
Therefore, the total number of different pizzas Maria's trattoria can make is 2^7 = 128 different combinations, including the option of a plain cheese pizza (where no additional toppings are chosen).