What is the simplified base for the function f(x) = 2(3√27^(2x))?

Solution:

Given, the function is f(x) = \(2(\sqrt[3]{(27)^{2x}})\)

We have to find the simplified base for the function.

By using the formula,

\((a^{m})^{n}=a^{mn}\)

27 can be written as (3)³.

\(2(\sqrt[3]{(27)^{2x}})\) = \(2(\sqrt[3]{(3^{3})^{2x}})\)

= \(2(\sqrt[3]{(3)^{6x}})\)

= \(2((3)^{6x})^{\frac{1}{3}}\)

= \(2(3)^{2x}\)

= \(2(9)^{x}\)

= \(18^{x}\)

Therefore, the simplified base for the function is 18.

What is the simplified base for the function f(x) = 2(3√27^(2x))?

Summary:

The simplified base for the function f(x) = 2(3√27^(2x)) is 18.