Question

What is the simplified base of the function f(x) = 1/4 (cube root of 108)^x?

Answer 1

about f(x)=1.19^x

hope it helps

Answer 2

Answer with explanation:

`\rightarrow f(x)=(1)/(4)* [(108)^{(1)/(3)}]^x\\\\\rightarrow f(x)=(1)/(4)* [(108)^{(x)/(3)}]\\\\\rightarrow f(x)=(1)/(4)* [(3^3 * 2^2)^{(x)/(3)}]\\\\\rightarrow f(x)=(3^x)/(2^2)* [(2)^{(2 x)/(3)}]\\\\\rightarrow f(x)=\frac{3^x}{2^{2 -(2 x)/(3)}}\\\\\rightarrow f(x)=(1)/(4) * [3* 2^{(2)/(3)}]^x}`

Used the following law of indices

`1. \rightarrow (x^a)^b=x^(ab)\\\\2.\rightarrow (x^a)/(x^b)=x^(a-b)`