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katrin [286]
3 years ago
10

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

Mathematics
2 answers:
son4ous [18]3 years ago
8 0

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.

Aleonysh [2.5K]3 years ago
3 0

Answer:

b

Step-by-step explanation:

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