Final answer:
The simplified base for the function f(x) = 2³√26²x is 2³ˣ√26². Hence the correct answer is option C
Step-by-step explanation:
The simplified base for the function f(x) = 2³√26²x is 2³ˣ√26².
To simplify the expression, first, rewrite the cube root as a fractional power:
f(x) = 2^(1/3) * 26²x
Next, combine the exponents:
f(x) = 2^(1/3 + 2) * x
Simplify the exponents:
f(x) = 2^(7/3) * x
Finally, the simplified base is 2^(7/3).
Hence the correct answer is option C