Cost of a dozen eggs depends on the size of the eggs. what is the dependent variable?

the cost of the eggs
cost (x) = x*price
this is an example of a proportional cost relation with the size been x 

the dependent variable is the cost of a dozen of eggs.

Explanation:

The cost is function of the size of the eggs, Cost = f (size).

That means that you introduce the size (this is the input) in the function an you obtain the cost (this is the output)

The input is the independent variable and the output is the dependent variable.

a - base

b - exponent

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8