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

[latex]a) 25 ^{ -frac{1}{2} } = (frac{1}{25})^{frac{1}{2}}=frac{1}{5}\ b) 243 ^{ frac{1}{5}}=(3^5)^{frac{1}{5}}=3\ c) 125 ^{ frac{2}{3} }= (5^3)^{frac{2}{3}}= 5^2=25\ d) 81 ^{ frac{3}{4} }= (3^4)^{frac{3}{4}}= 3^3=27\ e) ( frac{1}{64}) ^{- frac{2}{3} } } =64^{frac{2}{3}}=(4^3)^{frac{2}{3}}= 4^2=16[/latex] [latex]a) sqrt{8} - sqrt{32} + sqrt{128} = 2sqrt{2}-4sqrt{2}+8sqrt{2}=6sqrt{2} [/latex] [latex]a) ( sqrt{2} - sqrt{3} ) ^{2} = 2-2sqrt{6}+3= 5-2sqrt{6}\ b) ( sqrt{5} + sqrt{3}) ( sqrt{5} - sqrt{3}) = 5-3 = 2[/latex]

[latex]1) a) 25 ^{- frac{1}{2} } = frac{1}{ sqrt{25}}= oxed{ frac{1}{5}} \ \ b) 243^{ frac{1}{5}}= sqrt[5]{243}= sqrt[5]{3^5}= oxed{3} \ \ c) 125 ^{ frac{2}{3}} = sqrt[3]{125^2}= (sqrt[3]{5^3})^2= 5^2= oxed{25}\ \ d) 81 ^{ frac{3}{4}}= sqrt[4]{81^3}= (sqrt[4]{3^4})^3= 3^3 = oxed{27} \ \ e) ( frac{1}{64}) ^{- frac{2}{3} } = sqrt[3]{64^2}= ( sqrt[3]{2^6})^2 = 4^2= oxed{16}[/latex] [latex]2) a) sqrt{8} - sqrt{32} + sqrt{128} = \ \ sqrt{2^3} - sqrt{2^5} + sqrt{2^7}= \ \ 2 sqrt{2} -4 sqrt{2} +8 sqrt{2}= sqrt{2}( 2-4+8)= oxed{6 sqrt{2}} [/latex] [latex]3) a) ( sqrt{2} - sqrt{3} ) ^{2} = ( sqrt{2})^2-2* sqrt{2}* sqrt{3}+( sqrt{3})^2= 2-2 sqrt{2}* sqrt{3} + 3 \ \ 5-2 sqrt{2} sqrt{3}= oxed{5-2 sqrt{6}} \ \ \ b) ( sqrt{5} + sqrt{3}) ( sqrt{5} - sqrt{3}) = ( sqrt{5})^2- sqrt{15} + sqrt{15} - ( sqrt{3})^2 = \ \ 5-3= oxed{2} [/latex] pozdrowienia!!!!