1. Simplify: \( \begin{array}{l}\frac{9^{x}}{27^{x-1}} \\ \frac{3^{2} \times 7^{x-2} \times 3^{2 x}}{7^{5} \times 3^{4 x}} \\ \text { 2. } 3^{n-1}-4.3^{n+1} \\ \frac{5^{n}+5^{n-2}}{5^{n-5}}\end{array} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{5^{n}+5^{n-2}}{5^{n-5}}\) - step1: Add the terms: \(\frac{26\times 5^{n-2}}{5^{n-5}}\) - step2: Rewrite the expression: \(26\times 5^{3}\) - step3: Evaluate the power: \(26\times 125\) - step4: Multiply: \(3250\) Calculate or simplify the expression \( \frac{3^{2} \times 7^{x-2} \times 3^{2 x}}{7^{5} \times 3^{4 x}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{3^{2}\times 7^{x-2}\times 3^{2x}}{7^{5}\times 3^{4x}}\) - step1: Multiply by \(a^{-n}:\) \(3^{2}\times 7^{x-2}\times 3^{2x}\times 3^{-4x}\times 7^{-5}\) - step2: Multiply the terms: \(3^{2+2x-4x}\times 7^{x-2}\times 7^{-5}\) - step3: Subtract the terms: \(3^{2-2x}\times 7^{x-2}\times 7^{-5}\) - step4: Multiply the terms: \(3^{2-2x}\times 7^{x-2-5}\) - step5: Subtract the numbers: \(3^{2-2x}\times 7^{x-7}\) Calculate or simplify the expression \( 3^{n-1}-4 \cdot 3^{n+1} \). Simplify the expression by following steps: - step0: Solution: \(3^{n-1}-4\times 3^{n+1}\) - step1: Subtract the terms: \(-35\times 3^{n-1}\) Calculate or simplify the expression \( \frac{9^{x}}{27^{x-1}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{9^{x}}{27^{x-1}}\) - step1: Calculate: \(\frac{\left(3^{2}\right)^{x}}{27^{x-1}}\) - step2: Calculate: \(\frac{\left(3^{2}\right)^{x}}{\left(3^{3}\right)^{x-1}}\) - step3: Calculate: \(\frac{3^{2x}}{\left(3^{3}\right)^{x-1}}\) - step4: Calculate: \(\frac{3^{2x}}{3^{3x-3}}\) - step5: Calculate: \(3^{-x+3}\) Here are the simplified results for each expression: 1. For the expression \( \frac{9^{x}}{27^{x-1}} \): \[ \frac{9^{x}}{27^{x-1}} = 3^{-x+3} \] 2. For the expression \( \frac{3^{2} \times 7^{x-2} \times 3^{2x}}{7^{5} \times 3^{4x}} \): \[ \frac{3^{2} \times 7^{x-2} \times 3^{2x}}{7^{5} \times 3^{4x}} = 3^{2-2x} \times 7^{x-7} \] 3. For the expression \( 3^{n-1} - 4 \cdot 3^{n+1} \): \[ 3^{n-1} - 4 \cdot 3^{n+1} = -35 \times 3^{n-1} \] 4. For the expression \( \frac{5^{n}+5^{n-2}}{5^{n-5}} \): \[ \frac{5^{n}+5^{n-2}}{5^{n-5}} = 3250 \] These are the simplified forms of the given expressions.