# What is the simplified base of the function f(x) = 1/4root3 108^x?

Jul 14, 2018

$f \left(x\right) = {3}^{x}$

#### Explanation:

$f \left(x\right) = \frac{1}{4} \sqrt[3]{{108}^{x}}$

$\therefore f \left(x\right) = \frac{1}{4} \cdot {\left({108}^{x}\right)}^{\frac{1}{3}}$

$\therefore f \left(x\right) = \frac{1}{4} \cdot {108}^{\frac{x}{3}}$

$\therefore f \left(x\right) = {27}^{\frac{x}{3}}$

$\therefore f \left(x\right) = {\left({3}^{3}\right)}^{\frac{x}{3}}$

$\therefore f \left(x\right) = {3}^{x}$