Odpowiedź:
zad1
a)[tex]\frac{(-4)^2}{8^2} =(\frac{-4}{8} )^2=(-\frac{1}{2} )^2=\frac{1}{4}[/tex]
[tex]\frac{(0,55)^2}{(0,11)^2} =(\frac{0,55}{0,11} )^2=5^2=25[/tex]
[tex](-4,8)^6:(-4\frac{4}{5} )^6=[-4,8:(-4\frac{4}{5} )]^6=[-\frac{48}{10} *(-\frac{5}{24} )]^2=1^2=1[/tex]
b)[tex](-2,56:(\frac{16}{25} )^3=[-2,56:(\frac{16}{25} )]^3=(-\frac{256}{100} *\frac{25}{16} )^3=(-4)^3=-64[/tex]
[tex](-0,9)^2:(\frac{3}{8} )^2=[-0,9:(\frac{3}{8} )}]^2=[-\frac{9}{10} *\frac{8}{3} ]^2=(-\frac{12}{5} )^2=\frac{144}{25} =5\frac{19}{25}[/tex]
[tex](1\frac{2}{3} )^4:(-2\frac{7}{9} )^4=[1\frac{2}{3} :(-2\frac{7}{9} )]^4[/tex]
zad2
a)2²*25²=(2*25)²=50²=2500
16²*5²=(16*5)²=(80)²=6400
2⁴*50⁴=(2*50)⁴=100⁴=100 00 00 00
4³*25³=(4*25)³=100³=100 00 00
35²*2²=(35*2)=70²=49 00
b)[tex](-\frac{1}{4} )^2*16^2=(-\frac{1}{4} *16)^2=(-4)^2=16[/tex]
[tex](-2\frac{1}{2})^3 *(-4)^3=[-2\frac{1}{2} *(-4)]^3=[-\frac{5}{2} *(-4)]^3=10^3=1000[/tex]
(-0,1)⁵*10⁵=(-0,1*10)⁵=(-10)⁵=-1
(-1,5)²*(-8)²=[-1,5*(-8)]²=12²=144
c)[tex](\frac{1}{6} )^5*12=(\frac{1}{6} *12)^5=2^5=32[/tex]
[tex]7,5^3*(\frac{2}{3} )^3=(7,5*\frac{2}{3})^3 =(\frac{75}{10} *\frac{2}{3} )^3=5^3=125[/tex]
[tex](\frac{2}{7} )^8*3,5^8=(\frac{2}{7} *3,5)^8=1^8=1[/tex]
[tex]0,75^5*(2\frac{2}{3} )^5=(0,75*2\frac{2}{3} )^5=(\frac{75}{100} *\frac{8}{3} )^5=2^5=32[/tex]
10³*0,01³=(10*0,01)³=0,1³=0,001
d)[tex]2^3*3^3*(\frac{1}{6})^3=(2*3*\frac{1}{6})^3=1^3=1[/tex]
[tex](\frac{5}{3})^4 *(\frac{3}{4} )^4*4^4=(\frac{5}{3} *\frac{3}{4} *4)^4=5^4=625[/tex]
2,5⁵*4⁵*0,2⁵=(2,5*4*0,2)⁵=(10*0,2)⁵=2⁵=32
[tex](1\frac{1}{7} )^2*(\frac{1}{4} )^2*(\frac{14}{3} )^2=(1\frac{1}{7} *\frac{1}{4} *\frac{14}{3} )^2=(\frac{8}{7} *\frac{1}{4} *\frac{14}{3} )^2=(\frac{4}{3} )^2=\frac{16}{9} =1\frac{7}{9}[/tex]
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