(a) \( A=\frac{3^{n}-4}{2^{n} \cdot 3^{n}-2^{n} \cdot 2^{2}}= \)

Let's simplify the expression: \[ A = \frac{3^{n} - 4}{2^{n} \cdot 3^{n} - 2^{n} \cdot 2^{2}} \] **Step 1: Factor the Denominator** Notice that both terms in the denominator have a common factor of \(2^{n}\): \[ 2^{n} \cdot 3^{n} - 2^{n} \cdot 2^{2} = 2^{n} (3^{n} - 4) \] **Step 2: Simplify the Expression** Now, substitute the factored form of the denominator back into the expression for \(A\): \[ A = \frac{3^{n} - 4}{2^{n} (3^{n} - 4)} \] Assuming \(3^{n} \neq 4\), we can cancel out the common factor \((3^{n} - 4)\) from the numerator and the denominator: \[ A = \frac{1}{2^{n}} \] **Final Answer:** \[ A = \frac{1}{2^{n}} \quad \text{or equivalently} \quad A = 2^{-n} \]