Answer :

To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} (3)^x \)[/tex], we need to substitute [tex]\( x = 5 \)[/tex] into the function and simplify.

Given:
[tex]\[ f(x) = \frac{1}{9} (3)^x \][/tex]

We need to evaluate:
[tex]\[ f(5) = \frac{1}{9} (3)^5 \][/tex]

First, calculate [tex]\( 3^5 \)[/tex]:
[tex]\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \][/tex]

Next, substitute [tex]\( 3^5 \)[/tex] into the function:
[tex]\[ f(5) = \frac{1}{9} \times 243 \][/tex]

Now, simplify the expression:
[tex]\[ f(5) = \frac{243}{9} = 27 \][/tex]

Therefore, the value of [tex]\( f(5) \)[/tex] is:
[tex]\[ \boxed{27} \][/tex]

So, the correct answer is:
C. 27

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