Question

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

Answer 1

Answer:

Simplified base would be 3∛4

Step-by-step explanation:

Given exponential function,

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

Since, in an exponential function $f(x)=ab^x$

b is called base.

∵ 108 = 2 × 2 × 3 × 3 × 3,

Or 108 = 4 × 3³,

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

$\sqrt[3]{108}=\sqrt[3]{4}\times \sqrt[3](3^3)$  ( Using $\sqrt[n]{ab}=\sqrt[n]{a}\times \sqrt[n]{b}$ )

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

$\sqrt[3]{108}=\sqrt[3]{4}\times 3^{3\times \frac{1}{3}}$  ( Using power of power property of exponent )

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

Hence, the required simplified base would be 3∛4

i.e. SECOND option is correct.

Answer 2

Answer:

b

Step-by-step explanation: