To find the value of $f(1)$ given the function $f(x) = 6^{4x} + 8$, let's substitute $x = 1$ into the equation.

Step 1: Substitute $x = 1$ into the function

$f(1) = 6^{4(1)} + 8$ $f(1) = 6^{4} + 8$

Step 2: Compute $6^4$

$6^4 = 6 \times 6 \times 6 \times 6 = 1296$

Step 3: Add 8

$f(1) = 1296 + 8 = 1304$

Thus, the value of $f(1)$ is 1304.

Would you like further clarification or more examples on this?

Here are some related questions:

1. How would you find the value of $f(x)$ for other specific values of $x$?
2. What is the general behavior of exponential functions like $6^{4x}$?
3. How can you solve equations involving exponentiation and addition?
4. What is the importance of understanding exponential growth in real-world applications?
5. How does the function $f(x) = 6^{4x} + 8$ compare to simpler exponential functions like $f(x) = 6^x$?

Tip: When dealing with exponentiation in functions like $6^{4x}$, remember that the exponentiation is applied to the base first before any constants are added or subtracted.