What is the base of the exponent in the function $$ f(x)=3(\sqrt[3]{8})^{2 x} $$ when the function is written using only rational numbers and is in simplest form? w

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To find the base of the exponent in the function $$ f(x) = 3(\sqrt[3]{8})^{2x} $$, we need to simplify the expression $$ \sqrt[3]{8} $$ first.

1. **Calculate $$ \sqrt[3]{8} $$**:
   $$
   \sqrt[3]{8} = 8^{1/3}
   $$
   Since $$ 8 = 2^3 $$, we can rewrite it as:
   $$
   \sqrt[3]{8} = (2^3)^{1/3} = 2^{3 \cdot \frac{1}{3}} = 2^1 = 2
   $$

2. **Substitute back into the function**:
   Now we can substitute $$ \sqrt[3]{8} $$ back into the function:
   $$
   f(x) = 3(2)^{2x}
   $$

3. **Identify the base of the exponent**:
   The function can now be expressed as:
   $$
   f(x) = 3 \cdot 2^{2x}
   $$
   Here, the base of the exponent is $$ 2 $$.

Thus, the base of the exponent in the function $$ f(x) $$ when written in simplest form is $$ \boxed{2} $$.
The base of the exponent in the function $$ f(x) = 3(\sqrt[3]{8})^{2x} $$ is $$ 2 $$.

What is the base of the exponent in the function \( f(x)=3(\sqrt[3]{8})^{2 x} \) when the function is written using only rational numbers and is in simplest form? w

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