Question

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

Answer 1

Answer:

B.

Step-by-step explanation:

Answer 2

Answer:

The required simplified base would be 3∛4  

Step-by-step explanation:

Given exponential function that:

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

As we can see, 108 is the base of  the exponential function with the form:

f(x) = a$b^{x}$

So, we can factor 108 =  2 × 2 × 3 × 3 × 3

<=> 108 = 4 × 3³

Hence, $\sqrt[3]{108} = \sqrt[3]{4\times 3^3}$

So we have:

$\sqrt[3]{108}=\sqrt[3]{4}\times \sqrt[3](3^3)$

<=> $\sqrt[3]{108}=\sqrt[3]{4}\times (3^3)^\frac{1}{3}$

<=> $\sqrt[3]{108}=\sqrt[3]{4}\times 3^{3\times \frac{1}{3}}$

<=> $\sqrt[3]{108}=3\sqrt[3]{4}$

Hence, the required simplified base would be 3∛4