Odpowiedź:
Szczegółowe wyjaśnienie:
zadanie 4
a) [tex]0,04^{\frac{3}{2} } = (\frac{4}{100} )^{\frac{3}{2} } = \sqrt{(\frac{4}{100}) }^{3} = (\frac{1}{5})^3 = \frac{1}{125}[/tex]
b ) [tex](\frac{16}{100})^{-\frac{1}{2} } = (\frac{100}{16})^{\frac{1}{2} } = \sqrt{\frac{100}{16}} = \frac{10}{4} = \frac{5}{2}[/tex]
c) [tex](\frac{27}{1000})^{\frac{2}{3} } = \sqrt[3]{(\frac{27}{1000})} ^2 ={(\frac{3}{10})} ^2 = \frac{9}{100} = 0,09[/tex]
d) [tex](\frac{16}{10000})^{-\frac{3}{4} }= (\frac{10000}{16})^{\frac{3}{4} }= \sqrt[4]{(\frac{10000}{16})} ^{3} = (\frac{10}{2})^3 = 5^{3} = 125[/tex]
e) [tex](\frac{625}{10000})^{-\frac{5}{4} } = (\frac{10000}{625})^{\frac{5}{4} } = \sqrt[4]{(\frac{10000}{625})} ^{5} = (\frac{10}{5})^{5} = 2^{5} = 125[/tex]
f) [tex](\frac{32}{100000})^{\frac{3}{5} } = \sqrt[5]{(\frac{32}{100000})} ^{3} = (\frac{2}{10})^3 = \frac{8}{1000} = 0,008[/tex]
g) [tex](\frac{81}{10000} )^{-1,25} = (\frac{81}{10000} )^{-\frac{125}{100} }= (\frac{81}{10000} )^{-\frac{5}{4}} = = (\(\frac{10000}{81} )^{\frac{5}{4}} = \sqrt[4]{(\(\frac{10000}{81} )} ^ 5 = ( \frac{10}{3} ^5= \frac{100000}{243} = 411\frac{127}{243}[/tex]
h) [tex](\frac{256}{100000000})^{0,375} = (\frac{256}{100000000})^\frac{375}{1000} = (\frac{256}{100000000})^\frac{3}{8}= \sqrt[8]{(\frac{256}{100000000})} ^3 = (\frac{2}{10})^3 = \frac{8}{1000} = 0,008[/tex]
zadanie 5
a) [tex]2^{2} * 8^{\frac{2}{3} } = 2^{2} * \sqrt[3]{8} ^ 2= 2^{2} * 2^{2} = 2^{4}[/tex]
b) [tex]3^{3} * 27^{-\frac{4}{3} } = 3^{3} * \frac{1}{27} ^{\frac{4}{3} }= 3^{3} * \sqrt[3]{\frac{1}{27}} ^4= 3^{3} * (\frac{1}{3})^4 = 3^{3} * \frac{1}{81}= 27 * \frac{1}{81} = \frac{27}{81} = \frac{1}{3}[/tex]
c) [tex]0,008^{\frac{1}{3} } * \sqrt[3]{125} = ( \frac{8}{1000}) ^{\frac{1}{3} } * \sqrt[3]{125} = \sqrt[3]{( \frac{8}{1000})} * \sqrt[3]{125} = \frac{2}{10} * 5 = \frac{10}{10} = 1[/tex]
d) [tex]0,0256^{\frac{3}{4} } * (\sqrt[3]{10})^ 3= (\frac{256}{10000}) ^{\frac{3}{4} } * (\sqrt[3]{10})^ 3= \sqrt[4]{(\frac{256}{10000})} ^3 * (\sqrt[3]{10})^ 3= (\frac{4}{10})^3 * 10 = \frac{64}{1000} * 10 = \frac{640}{1000} =\frac{64}{100} = 0,64[/tex]
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Odpowiedź:
Szczegółowe wyjaśnienie:
zadanie 4
a) [tex]0,04^{\frac{3}{2} } = (\frac{4}{100} )^{\frac{3}{2} } = \sqrt{(\frac{4}{100}) }^{3} = (\frac{1}{5})^3 = \frac{1}{125}[/tex]
b ) [tex](\frac{16}{100})^{-\frac{1}{2} } = (\frac{100}{16})^{\frac{1}{2} } = \sqrt{\frac{100}{16}} = \frac{10}{4} = \frac{5}{2}[/tex]
c) [tex](\frac{27}{1000})^{\frac{2}{3} } = \sqrt[3]{(\frac{27}{1000})} ^2 ={(\frac{3}{10})} ^2 = \frac{9}{100} = 0,09[/tex]
d) [tex](\frac{16}{10000})^{-\frac{3}{4} }= (\frac{10000}{16})^{\frac{3}{4} }= \sqrt[4]{(\frac{10000}{16})} ^{3} = (\frac{10}{2})^3 = 5^{3} = 125[/tex]
e) [tex](\frac{625}{10000})^{-\frac{5}{4} } = (\frac{10000}{625})^{\frac{5}{4} } = \sqrt[4]{(\frac{10000}{625})} ^{5} = (\frac{10}{5})^{5} = 2^{5} = 125[/tex]
f) [tex](\frac{32}{100000})^{\frac{3}{5} } = \sqrt[5]{(\frac{32}{100000})} ^{3} = (\frac{2}{10})^3 = \frac{8}{1000} = 0,008[/tex]
g) [tex](\frac{81}{10000} )^{-1,25} = (\frac{81}{10000} )^{-\frac{125}{100} }= (\frac{81}{10000} )^{-\frac{5}{4}} = = (\(\frac{10000}{81} )^{\frac{5}{4}} = \sqrt[4]{(\(\frac{10000}{81} )} ^ 5 = ( \frac{10}{3} ^5= \frac{100000}{243} = 411\frac{127}{243}[/tex]
h) [tex](\frac{256}{100000000})^{0,375} = (\frac{256}{100000000})^\frac{375}{1000} = (\frac{256}{100000000})^\frac{3}{8}= \sqrt[8]{(\frac{256}{100000000})} ^3 = (\frac{2}{10})^3 = \frac{8}{1000} = 0,008[/tex]
zadanie 5
a) [tex]2^{2} * 8^{\frac{2}{3} } = 2^{2} * \sqrt[3]{8} ^ 2= 2^{2} * 2^{2} = 2^{4}[/tex]
b) [tex]3^{3} * 27^{-\frac{4}{3} } = 3^{3} * \frac{1}{27} ^{\frac{4}{3} }= 3^{3} * \sqrt[3]{\frac{1}{27}} ^4= 3^{3} * (\frac{1}{3})^4 = 3^{3} * \frac{1}{81}= 27 * \frac{1}{81} = \frac{27}{81} = \frac{1}{3}[/tex]
c) [tex]0,008^{\frac{1}{3} } * \sqrt[3]{125} = ( \frac{8}{1000}) ^{\frac{1}{3} } * \sqrt[3]{125} = \sqrt[3]{( \frac{8}{1000})} * \sqrt[3]{125} = \frac{2}{10} * 5 = \frac{10}{10} = 1[/tex]
d) [tex]0,0256^{\frac{3}{4} } * (\sqrt[3]{10})^ 3= (\frac{256}{10000}) ^{\frac{3}{4} } * (\sqrt[3]{10})^ 3= \sqrt[4]{(\frac{256}{10000})} ^3 * (\sqrt[3]{10})^ 3= (\frac{4}{10})^3 * 10 = \frac{64}{1000} * 10 = \frac{640}{1000} =\frac{64}{100} = 0,64[/tex]