Question

What is the simplified base of the function f(x) = One-fourth (Root Index 3 StartRoot 108 EndRoot) Superscript x?

Answer 1

Answer:

The base is: $3 \sqrt[3]{4}$

Step-by-step explanation:

Given

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

Required

The base

Expand 108

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

Rewrite the exponent as:

$f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x$

Expand

$f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x$

$f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x$

Rewrite as:

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

An exponential function has the following form:

$f(x)=ab^x$

Where

$b \to base$

By comparison:

$b =3 \sqrt[3]{4}$

So, the base is: $3 \sqrt[3]{4}$