Final answer:
The expression for f(x) when we rewrite 64ˣ over 4⁵ˣ⁻¹ as 4ᶠ^(ˣ^) is 4^(58x).
Step-by-step explanation:
The expression for f(x) when we rewrite 64ˣ over 4⁵ˣ⁻¹ as 4ᶠ^(ˣ^) is 4^(64x - 5x - x).
To simplify this expression, we can combine the exponents and get 4^(58x). This means that the expression f(x) is equal to 4 raised to the power of 58x.
For example, if x is 2, then f(x) would be 4^(58*2), which is equal to 4^116.