The simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
How to simplify the base function?
The function is given as:
[tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex]
Expand 108
[tex]f(x) = \frac 14(\sqrt[3]{27 * 4})^x[/tex]
Take the cube root of 27
[tex]f(x) = \frac 14 * 3^x(\sqrt[3]{4})^x[/tex]
Evaluate the product
[tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
Hence, the simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
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