find the expression 67x5x can be written as 6 f x where f x

find the expression (6^7x)^5x can be written as 6 ^{f (x)}, where f (x) is a function of x. Find f(x).

Solution

When you have a power to a power, you multiply the exponents. For example,
(x^a)^b = x^(a*b).

So in your problem, you would get:
(6^(7x))^(5x) = 6^(7x*5x) = 6^(35x^2)

Since the function f(x) is just referring to the exponent on the 6, your answer would then be:
f(x) = 35x^2