find the expression

Question

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

Answer 1

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

 

Make sense?