Question

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

3

3RootIndex 3 StartRoot 4 EndRoot

6RootIndex 3 StartRoot 3 EndRoot

27

Answer: second choice

Answer 1

b

Explanation:

Answer 2

Simplified base would be 3∛4

Explanation:

Given exponential function,

`f(x)=(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* 3^3}`

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

`\sqrt[3]{108}=\sqrt[3]{4}* (3^3)^(1)/(3)`

`\sqrt[3]{108}=\sqrt[3]{4}* 3^{3* (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.