If `3^(3x)=(9)/(3^(x))`, find the value of `x`.

Explanation

To solve the equation \( 3^{3x} = \frac{9}{3^x} \), we will follow these steps:

### Step 1: Rewrite 9 as a power of 3
We know that \( 9 = 3^2 \). Therefore, we can rewrite the equation as:
\[ 3^{3x} = \frac{3^2}{3^x} \]

### Step 2: Simplify the right-hand side
Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify the right-hand side:
\[ 3^{3x} = 3^{2 - x} \]

### Step 3: Set the exponents equal to each other
Since the bases are the same (both are base 3), we can set the exponents equal to each other:
\[ 3x = 2 - x \]

### Step 4: Solve for x
Now, we will solve for \( x \):
1. Add \( x \) to both sides:
\[ 3x + x = 2 \]
This simplifies to:
\[ 4x = 2 \]

2. Divide both sides by 4:
\[ x = \frac{2}{4} \]
This simplifies to:
\[ x = \frac{1}{2} \]

### Final Answer
The value of \( x \) is:
\[ \boxed{\frac{1}{2}} \]