What is the simplified base for the function $$ f(x)=2\left(\sqrt{27}^{2 x}\right) $$ ? 3 9 18 9

Question

UpStudy AI · Accepted Answer

To simplify the base of the function $$ f(x) = 2\left(\sqrt{27}^{2x}\right) $$, follow these steps:

1. **Simplify $$\sqrt{27}$$:**
   $$
   \sqrt{27} = 27^{1/2} = (3^3)^{1/2} = 3^{3/2}
   $$

2. **Raise $$\sqrt{27}$$ to the power of $$2x$$:**
   $$
   \left(\sqrt{27}\right)^{2x} = \left(3^{3/2}\right)^{2x} = 3^{3x}
   $$

3. **Express the function with the simplified base:**
   $$
   f(x) = 2 \cdot 3^{3x}
   $$
   Here, the base is $$3$$.

So, the **simplified base** for the function $$ f(x) = 2\left(\sqrt{27}^{2x}\right) $$ is **3**.

**Answer:** 3
The simplified base for the function $$ f(x) = 2\left(\sqrt{27}^{2x}\right) $$ is **3**.

What is the simplified base for the function \( f(x)=2\left(\sqrt{27}^{2 x}\right) \) ? 3 9 18 9