Oblicz: a) [latex]frac{1}{5}^{-1} + frac{1}{5}^{-2} = ?[/latex] b) [latex]( frac{1}{3} - frac{1}{2})^{-1} = ?[/latex] c) [latex]( frac{1}{3} - frac{1}{5} )^{-3} : ( frac{1}{5} + frac{1}{3})^{-3}[/latex]

a) ......... = 5^1 + 5^2 = 5 + 25 = 30 b) ..... = (2/6 - 3/6)^(-1) = (-1/6)^(-1) = -6 c) ..... = (5/15 - 3/15)^(-3) : (3/15 + 5/15)^(-3) = (2/15)^(-3) : (8/15)^(-3) = (15/2)^3 : (15/8)^3 = (15/2 : 15/8)^3 = (15/2 * 8/15)^3 = 4^3 = 64

[latex]a)\ (frac{1}{5})^{-1} + (frac{1}{5})^{-2} =5^1 + 5^2=5+25=30 \ \b)\ ( frac{1}{3} - frac{1}{2})^{-1} =(frac{2}{6}-frac{3}{6})^{-1} = (-frac{1}{6})^{-1} =-6\ \c)\ ( frac{1}{3} - frac{1}{5} )^{-3} : ( frac{1}{5} + frac{1}{3})^{-3}=(frac{5}{15}-frac{3}{15})^{-3}:(frac{3}{15}+frac{5}{15})^{-3}=(-frac{2}{15})^{-3}:(frac{8}{15})^{-3}=\ \=(-frac{2}{15} : frac{8}{15})^{-3}=(-frac{2}{15}cdot frac{15}{8})^{-3} = (-frac{2}{8})^{-3}=(-frac{1}{4})^{-3}=4^3=64 [/latex]

oblicz wartość wyrażenia a)[latex] (frac{2}{3})^{5}*(frac{3}{4})^{5} [/latex] b)[latex] (frac{1}{2})^{4}*(frac{2}{3})^{4} [/latex] c)[latex] (1frac{1}{2})^{50}*(frac{2}{3})^{50} [/latex] d)[latex] (2frac{1}{3})^{4}*(frac{6}{7})^{4} [/latex]

oblicz wartość wyrażenia a)[latex] (frac{2}{3})^{5}*(frac{3}{4})^{5} [/latex] b)[latex] (frac{1}{2})^{4}*(frac{2}{3})^{4} [/latex] c)[latex] (1frac{1}{2})^{50}*(frac{2}{3})^{50} [/latex] d)[latex] (2frac{1}{3})^{4}*(frac{6}{7})^{4} [/latex]...

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