Math Problem Statement
Given f(n) = 3(2^n)^3, f(5) = ?
Solution
The problem requires us to evaluate the function at .
Let's rewrite the function to make it simpler to understand:
This can be further simplified to:
Now, substitute :
Calculating :
Thus,
So, the value of is 98,304.
Would you like more details or have any questions? Here are 5 related questions you might be interested in:
- How do you simplify expressions involving exponents and powers?
- What is the general approach to solving exponential functions?
- How do exponential functions differ from linear functions?
- Can you provide more examples of evaluating exponential functions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Exponents
Functions
Algebra
Formulas
f(n) = 3(2^n)^3
f(5) = 3(2^5)^3
Theorems
-
Suitable Grade Level
Grades 9-12