Simplify fully wilhout using a caleulator. Your answer must be free of negative exponents and irrational denominators. \( 2.1 .1 \quad 64^{-\frac{2}{3}} \) \( 2.1 .2 \frac{3^{2 n+2}-9^{n-1}}{2.3^{2 n+1}} \) \( 2.1 .3 \quad \frac{(3-\sqrt{3})^{2}}{\sqrt{3} \cdot \sqrt{6}} \)

Calculate or simplify the expression \( 64^{-\frac{2}{3}} \). Calculate the value by following steps: - step0: Calculate: \(64^{-\frac{2}{3}}\) - step1: Express with a positive exponent: \(\frac{1}{64^{\frac{2}{3}}}\) - step2: Evaluate the power: \(\frac{1}{16}\) Calculate or simplify the expression \( \frac{3^{2n+2}-9^{n-1}}{2*3^{2n+1}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{3^{2n+2}-9^{n-1}}{2\times 3^{2n+1}}\) - step1: Subtract the terms: \(\frac{80\times 3^{2n-2}}{2\times 3^{2n+1}}\) - step2: Reduce the fraction: \(\frac{40}{3^{3}}\) - step3: Evaluate the power: \(\frac{40}{27}\) Calculate or simplify the expression \( \frac{(3-\sqrt{3})^{2}}{\sqrt{3} \cdot \sqrt{6}} \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(3-\sqrt{3}\right)^{2}}{\sqrt{3}\times \sqrt{6}}\) - step1: Multiply the numbers: \(\frac{\left(3-\sqrt{3}\right)^{2}}{3\sqrt{2}}\) - step2: Evaluate the power: \(\frac{12-6\sqrt{3}}{3\sqrt{2}}\) - step3: Reduce the fraction: \(\frac{4-2\sqrt{3}}{\sqrt{2}}\) - step4: Multiply by the Conjugate: \(\frac{\left(4-2\sqrt{3}\right)\sqrt{2}}{\sqrt{2}\times \sqrt{2}}\) - step5: Multiply the numbers: \(\frac{4\sqrt{2}-2\sqrt{6}}{\sqrt{2}\times \sqrt{2}}\) - step6: Multiply the numbers: \(\frac{4\sqrt{2}-2\sqrt{6}}{2}\) - step7: Rewrite the expression: \(\frac{2\left(2\sqrt{2}-\sqrt{6}\right)}{2}\) - step8: Reduce the fraction: \(2\sqrt{2}-\sqrt{6}\) The simplified forms of the given expressions are: 1. \(64^{-\frac{2}{3}} = \frac{1}{16} = 0.0625\) 2. \(\frac{3^{2n+2}-9^{n-1}}{2*3^{2n+1}} = \frac{40}{27} = 1\frac{13}{27} = 1.4881\) 3. \(\frac{(3-\sqrt{3})^{2}}{\sqrt{3} \cdot \sqrt{6}} = 2\sqrt{2}-\sqrt{6}\)