Question

What is the simplified base of the function f(x)=1/4(D" id="TexFormula1" title="\sqrt[3]{108} ^{x\\}" alt="\sqrt[3]{108} ^{x\\}" align="absmiddle" class="latex-formula">)

Answer 1

The simplified function of $f(x) = \frac 14(\sqrt[3]{108^x})$ is $f(x) = \frac {3^x}4(\sqrt[3]{4})^x$

How to simplify the base function?

The function is given as:

$f(x) = \frac 14(\sqrt[3]{108^x})$

Expand 108

$f(x) = \frac 14(\sqrt[3]{27 * 4})^x$

Take the cube root of 27

$f(x) = \frac 14 * 3^x(\sqrt[3]{4})^x$

Evaluate the product

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

Hence, the simplified function of $f(x) = \frac 14(\sqrt[3]{108^x})$ is $f(x) = \frac {3^x}4(\sqrt[3]{4})^x$

Read more about functions at:

brainly.com/question/12431044

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