Cześć!
Szczegółowe wyjaśnienie:
Zadanie 6.
Podnieś do potęgi
a)
[tex](2x) {}^{6} = 64x{}^{6}[/tex]
b)
[tex]( - 3x {}^{2} ) {}^{2} = 3 {}^{2} \cdot \: (x {}^{2} ) {}^{2} = 9x {}^{4} [/tex]
c)
[tex](x {}^{7} y {}^{3} ) {}^{3} = (x {}^{7} ) {}^{3} \cdot(y {}^{3} ) {}^{3} = x {}^{21} y {}^{9} [/tex]
d)
[tex]( \frac{ - 5x {}^{5} }{2y} ) {}^{3} = \frac{ ( - 5x {}^{5}) {}^{3} }{(2y)} {}^{3} = - \frac{(5x {}^{5}) {}^{3} }{(2y) {}^{3} } = - \frac{ 125x {}^{15} }{8y {}^{3} } [/tex]
Zadanie 7.
Oblicz.
[tex] \frac{2 {}^{10} }{125} \cdot \frac{5 {}^{6} }{128} = \frac{2 {}^{10} }{5 {}^{3} } \cdot \frac{5 {}^{6} }{2 {}^{7} } = 2 {}^{3} \cdot5 {}^{3} = 10 {}^{3} [/tex]
Zadanie 8.
a)
[tex]81 {}^{4} : 27 {}^{4} = 3 {}^{16} : 3 {}^{12} = 3 {}^{16 - 12} = 3 {}^{4} [/tex]
b)
[tex]2 \frac{1}{2} ) {}^{10} \cdot( \frac{3}{7} ) {}^{10} = (2 \frac{1}{2} \cdot \frac{3}{7} ) {}^{10} = ( \frac{5}{2} \cdot \frac{3}{7} ) {}^{10} = ( \frac{15}{14} ) {}^{10} = \frac{15 {}^{10} }{14 {}^{10} } [/tex]
c)
[tex]( - 0.8) {}^{4} : 8 {}^{4} = 0.8 {}^{4} : 8 {}^{4} = (0.8 : 8) {}^{4} = 0.1 {}^{4} = ( \frac{1}{10} ) {}^{4} = \frac{1}{10000} [/tex]
d)
[tex]( - \frac{5}{12} ) {}^{3} :( \frac{1}{12} ) {}^{3} = - ( \frac{5}{12} ) {}^{3} :( \frac{1}{12} ) {}^{3} = - ( \frac{5}{12} : \frac{1}{12} ) {}^{3} = - ( \frac{5}{12} \cdot12) {}^{3} = - 5 {}^{3} = - 125[/tex]
Zadanie 9.
[tex] \frac{81}{8 {}^{3} } \cdot \frac{2 {}^{15} }{3 {}^{10} } = \frac{3 {}^{4} }{2 {}^{9} } \cdot \frac{2 {}^{15} }{3 {}^{10} } = 3 {}^{4} \cdot \frac{2 {}^{6} }{2 {}^{10} } = \frac{2 {}^{6} }{3 {}^{6} } = \frac{64}{3 {}^{6} } = \frac{64}{729} [/tex]
