Oblicz. a) [latex] (frac{3}{2} )^{-6} . (frac{3}{2} )^{2} . frac{ 9^{4} }{ 8^{3} } =[/latex] b) [latex] 10^{4} . ( frac{4}{5} )^{-3} . ( 5^{5} ) ^{-1} =[/latex] c) [latex] 2^{-5} . ( frac{1}{ sqrt{2} } ) ^{-4} . sqrt{8} ^{6} [/latex] =

a)[latex](frac{3}{2})^{-6}*(frac{3}{2})^{2}*frac{9^{4}}{8^{3}}=(frac{3}{2})^{-6+2}*frac{(3^{2})^{4}}{(2^{3})^{3}}=frac{3^{-4}}{2^{-4}}*frac{3^{8}}{2^{9}}=frac{3^{4}}{2^{5}}[/latex] b)[latex]10^{4}*(frac{4}{5})^{-3}*(5^{5})^{-1}=10^{4}*frac{4^{-3}}{5^{-3}}*frac{1}{5^{5}}=2^{4}*5^{4}*frac{4^{-3}}{5^{2}}=2^{4}*5^{2}*frac{1}{2^{6}}=frac{5^{2}}{2^{2}}[/latex] c)[latex]2^{-5}*(frac{1}{sqrt{2}})^{-4}*sqrt{8}^{6}=2^{-5}*2^{2}*(2^{3})^{3}=2^{-5+2+9}=2^{6}[/latex]

[latex]a) (frac{3}{2} )^{-6} . (frac{3}{2} )^{2} . frac{ 9^{4} }{ 8^{3} } = \ \(frac{3}{2} )^{-6} . (frac{3}{2} )^{2} . frac{ (3^2)^{4} }{ (2^3)^{3} } = \ \ (frac{3}{2} )^{-6} . (frac{3}{2} )^{2} . frac{ 3^{8} }{ 2^{9} } = dfrac{3^{-6+2+8}}{2 ^{-6+2+9}}= dfrac{3^4}{2^5}= oxed{ frac{81}{32}} [/latex] [latex]b) 10^{4} * ( frac{4}{5} )^{-3}* ( 5^{5} ) ^{-1} = \ \ (2*5)^{4} * ( frac{4}{5} )^{-3} * ( 5^{-5} ) =\ \ 2^4*5^{4} * ( frac{2^2}{5} )^{-3}* ( 5^{-5} ) =\ \ 2^ {4}*5^{4}* ( frac{5^3}{2^6} )* ( 5^{-5} ) =2^{4-6}*5 ^{4+3+(-5)}=2^{-2}*5 ^{2}= frac{1}{4}*25= oxed{ frac{25}{4}} \ \ \ [/latex] [latex]c) 2^{-5} * ( frac{1}{ sqrt{2} } ) ^{-4} * sqrt{8} ^{6} = \ \ 2^{-5} * ( sqrt{2} } ) ^{4} * sqrt{2^3} ^{6} = \ \ 2^{-5} * ( sqrt{2} } ) ^{4} * sqrt{2} ^{18} =\ \ 2^{-5} * 2^{2} * 2 ^{9} =2^{-5+2+9}= 2^6= oxed{64} \ \ [/latex]

Oblicz: a) 25⁻[latex] ^{ frac{1}{2} } [/latex] b) 243[latex] ^{ frac{1}{5} [/latex] c) 125[latex] ^{ frac{2}{3} [/latex] d) 81 [latex] ^{ frac{3}{4} [/latex] e) [latex]( frac{1}{64})[/latex]⁻[latex] ^{ frac{2}{3} } [/latex] Doprowadź do najprostsze

Oblicz: a) 25⁻[latex] ^{ frac{1}{2} } [/latex] b) 243[latex] ^{ frac{1}{5} [/latex] c) 125[latex] ^{ frac{2}{3} [/latex] d) 81 [latex] ^{ frac{3}{4} [/latex] e) [latex]( frac{1}{64})[/latex]⁻[latex] ^{ frac{2}{3} } [/latex] Doprowadź do ...

Oblicz [latex] (frac{3}{2}) ^{-6} * (frac{3}{2}) ^{2} * frac{ 9^{4} }{ 8^{3} } [/latex] [latex] 10^{4} * (frac{4}{5})^{-3} * (5^{5)}^{-1} [/latex] [latex] 2^{-5} * (frac{1}{ sqrt{2} })^{-4} * sqrt{8}^{6} [/latex]

Oblicz [latex] (frac{3}{2}) ^{-6} * (frac{3}{2}) ^{2} * frac{ 9^{4} }{ 8^{3} } [/latex] [latex] 10^{4} * (frac{4}{5})^{-3} * (5^{5)}^{-1} [/latex] [latex] 2^{-5} * (frac{1}{ sqrt{2} })^{-4} * sqrt{8}^{6} [/latex]...

Oblicz granice a) [latex] lim_{x o 3} frac{ sqrt{ x^{2}-3x+9 } }{x+2} [/latex] b) [latex] lim_{x o-3} frac{9+3x}{2x+6} [/latex] c) [latex] lim_{x o 9 } frac{x-9}{ sqrt{x} -3} [/latex]

Oblicz granice a) [latex] lim_{x o 3} frac{ sqrt{ x^{2}-3x+9 } }{x+2} [/latex] b) [latex] lim_{x o-3} frac{9+3x}{2x+6} [/latex] c) [latex] lim_{x o 9 } frac{x-9}{ sqrt{x} -3} [/latex]...

Oblicz granice a) [latex] lim_{x o 0} frac{ sqrt{6 x^{2} -10x+9} }{ x^{2} +4} [/latex] b) [latex] lim_{x o 2} frac{8x-16}{-11x+22} [/latex] c) [latex] lim_{x o 16} frac{ sqrt{x} -4}{x-16} [/latex]

Oblicz granice a) [latex] lim_{x o 0} frac{ sqrt{6 x^{2} -10x+9} }{ x^{2} +4} [/latex] b) [latex] lim_{x o 2} frac{8x-16}{-11x+22} [/latex] c) [latex] lim_{x o 16} frac{ sqrt{x} -4}{x-16} [/latex]...

usuń niewymierność z mianowników i oblicz wartość wyrażenia:[latex]frac{4}{sqrt{2}}+ frac{6}{sqrt{2}-2}- frac{3- 2sqrt{2}}{3+2sqrt{2}}[/latex]. Pilne!! Potrzebne na jutro, z góry dziękuję..

usuń niewymierność z mianowników i oblicz wartość wyrażenia:[latex]frac{4}{sqrt{2}}+ frac{6}{sqrt{2}-2}- frac{3- 2sqrt{2}}{3+2sqrt{2}}[/latex]. Pilne!! Potrzebne na jutro, z góry dziękuję.....