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The problem requires us to evaluate the function \( f(n) = 3(2^n)^3 \) at \( n = 5 \). 

Let's rewrite the function to make it simpler to understand:

\[
f(n) = 3(2^n)^3
\]

This can be further simplified to:

\[
f(n) = 3 \cdot (2^n)^3 = 3 \cdot 2^{3n}
\]

Now, substitute \( n = 5 \):

\[
f(5) = 3 \cdot 2^{3 \times 5} = 3 \cdot 2^{15}
\]

Calculating \( 2^{15} \):

\[
2^{15} = 32768
\]

Thus,

\[
f(5) = 3 \cdot 32768 = 98304
\]

So, the value of \( f(5) \) is **98,304**.

Would you like more details or have any questions? Here are 5 related questions you might be interested in:

1. How do you simplify expressions involving exponents and powers?
2. What is the general approach to solving exponential functions?
3. How do exponential functions differ from linear functions?
4. Can you provide more examples of evaluating exponential functions?
5. How does the growth rate of an exponential function compare to that of a polynomial function?

**Tip:** When evaluating functions, always simplify the expression first before substituting values to avoid errors.

Learn how to evaluate the function f(n) = 3(2^n)^3 at n = 5. This step-by-step guide covers exponent simplification and function evaluation, making it suitable for high school algebra students.

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