Definition of average rate of change a function g(x) over an interval [a,b]:
[tex]A = \dfrac{g(b)-g(a)}{b-a}[/tex]
Substitute your function and your interval:
[tex]A = \dfrac{(3^6-6)-(3^0-6)}{3-0} = \dfrac{3^6-6-3^0+6}{3} = \dfrac{3^6-1}{3} = \dfrac{728}{3}[/tex]
