Answer with explanation:
[tex]\rightarrow f(x)=\frac{1}{4}\times [(108)^{\frac{1}{3}}]^x\\\\\rightarrow f(x)=\frac{1}{4}\times [(108)^{\frac{x}{3}}]\\\\\rightarrow f(x)=\frac{1}{4}\times [(3^3 \times 2^2)^{\frac{x}{3}}]\\\\\rightarrow f(x)=\frac{3^x}{2^2}\times [(2)^{\frac{2 x}{3}}]\\\\\rightarrow f(x)=\frac{3^x}{2^{2 -\frac{2 x}{3}}}\\\\\rightarrow f(x)=\frac{1}{4} \times [3\times 2^{\frac{2}{3}}]^x}[/tex]
Used the following law of indices
[tex]1. \rightarrow (x^a)^b=x^{ab}\\\\2.\rightarrow \frac{x^a}{x^b}=x^{a-b}[/tex]
