Final answer:
The simplified base for the function f(x) = 2(3/27²x) is 3², which equals 9 after applying the rules of exponents for division.
Step-by-step explanation:
To find the simplified base for the function f(x) = 2(3/27²x), first, we must simplify the expression inside the parentheses.
The number 27 is equal to 3³, so we can rewrite the expression as 3/3³²x.
When simplifying, we must remember the rules of exponents, which state that when dividing bases that are the same, we subtract the exponents.
Therefore, 3¹/3¶²x becomes 3¹³²x or 3³²x, simplifying further to 3¹²x or just 3²x.
The simplified base is therefore 3² or 9.