9.5 [latex]a) 2^{sqrt{2}}=2,665\ b) 5^{sqrt{2}} = 9,739\ c) (sqrt{2})^{sqrt{2}}=1,633\ d) 2^{pi} = 8,825\ e) 3^{pi} = 31,544\ f) (sqrt{5})^{pi} = 12,530[/latex] 9.6 [latex]a) a^{frac{1}{2}} cdot a^{frac{1}{4}} = a^{frac{1}{2}+frac{1}{4}}=a^{frac{3}{4}}\ \ b) x^{frac{1}{2}}sqrt{x} = x^{frac{1}{2}} cdot x^{frac{1}{2}} =x^{frac{1}{2}+frac{1}{2}}=x^1=x\ \ c) a^{frac{1}{m}} cdot a^{frac{1}{n}} cdot a^{frac{1}{r}} =a^{frac{1}{m}+frac{1}{n}+frac{1}{r}} = a^{frac{nr+mr+mn}{mnr}}\ \ d) a^{frac{1}{n}}b^{frac{1}{m}}cdot a^{-frac{1}{n}}b^{frac{2}{m}}=a^{frac{1}{n}-frac{1}{n}}b^{frac{1}{m}+frac{2}{m}}=a^0b^{frac{3}{m}}=b^{frac{3}{m}}\ \ [/latex] [latex]e) a^{frac{1}{2}}:a^{frac{1}{4}}=a^{frac{1}{2}-frac{1}{4}}=a^{frac{1}{4}}\ \ f) frac{x^{frac{7}{15}}}{x^{frac{1}{5}}}=x^{frac{7}{15}}:x^{frac{7}{5}} = x^{frac{7}{15}-frac{7}{5}}=x^{-frac{14}{15}}=frac{1}{x^{frac{14}{15}}}\ \ g) frac{a^{frac{7}{8}}}{sqrt[4]{a^3}}=frac{a^{frac{7}{8}}}{a^{frac{3}{4}}}}=a^{frac{7}{8}}:a^{frac{3}{4}} = a^{frac{1}{8}}\ \ h) a^{frac{1}{2}}b^{frac{1}{2}}=(ab)^{frac{1}{2}}\ \ [/latex] [latex]i) frac{a^{frac{7}{8}}}{b^{frac{7}{8}}} = (frac{a}{b})^{frac{7}{8}} \ \ j) (a^{-frac{2}{3}}b^4)^{frac{12}{5}} =a^{-frac{2}{3}cdot frac{12}{5}}b^{4cdot frac{12}{5}}=a^{-frac{8}{5}}b^{frac{48}{5}}[/latex]
