what is the simplified base for the function $f(x)=2(sqrt3{27^{2x}})$?\n2\n3\n9\n18

Explanation:

Step1: Simplify the cube - root part

First, simplify $\sqrt[3]{27^{2x}}$. Since $27 = 3^3$, then $\sqrt[3]{27^{2x}}=(3^3)^{ \frac{2x}{3}}$.

Step2: Apply the power - of - a - power rule

Using the power - of - a - power rule $(a^m)^n=a^{mn}$, we have $(3^3)^{\frac{2x}{3}} = 3^{3\times\frac{2x}{3}}=3^{2x}$.

Step3: Analyze the function

The function $f(x)=2(\sqrt[3]{27^{2x}})$ becomes $f(x)=2\times3^{2x}$. The base of the exponential part is 3.

Answer:

B. 3