To solve the equation \( 3^{-2x+1} \cdot 3^{-2x-3} = 3^{-3} \), we can start by simplifying the left-hand side using the properties of exponents. The property states that \( a^m \cdot a^n = a^{m+n} \).
So, we can combine the exponents on the left side:
\[ 3^{-2x+1} \cdot 3^{-2x-3} = 3^{(-2x + 1) + (-2x - 3)} = 3^{-4x - 2} \]
Now our equation looks like this:
\[ 3^{-4x - 2} = 3^{-3} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ -4x - 2 = -3 \]
Now, let's solve for \( x \):
- Add 2 to both sides:
\[ -4x = -1 \]
- Divide both sides by -4:
\[ x = \frac{1}{4} \]
Therefore, the solution for \( x \) is \( x = \frac{1}{4} \).
The correct answer is B. X = 1/4.
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