Zadanie 2
a)
4^{-2}*15^{-2}=(4*15)^{-2}=60^{-2}=(\frac{1}{60})^2=\frac{1}{3600}
b)
2^{-6}*5^{-6}=(2*5)^{-6}=10^{-6}=(\frac{1}{10})^6=\frac{1}{1000000}=0,000001
c)
(\frac{1}{4})^{-5}*8^{-5}=(\frac{1}{\not4^1}*\not8^2)^{-5}=(\frac{2}{1})^{-5}=(\frac{1}{2})^5=\frac{1}{32}
d)
2,8^{-1}*10^{-1}=(2,8*10)^{-1}=28^{-1}=(\frac{1}{28})^1=\frac{1}{28}
e)
(\frac{3}{5})^{-2}:(1\frac{2}{3})^{-2}=(\frac{3}{5}:\frac{5}{3})^{-2}=(\frac{3}{5}*\frac{3}{5})^{-2}=[(\frac{3}{5})^2]^{-2}=(\frac{3}{5})^{-4}=(\frac{5}{3})^4=\frac{625}{81}=7\frac{58}{81}
f)
(-0,15)^{-3}*6^{-3}=(-0,15*6)^{-3}=(-0,9)^{-3}=(-\frac{9}{10})^{-3}=(-\frac{10}{9})^3=-\frac{1000}{729}=-1\frac{271}{729}
g)
(1\frac{1}{4})^{-8}*0.8^{-8}=(\frac{\not5^1}{\not4^1}*\frac{\not8^2}{\not10^2})^{-8}=(\frac{2}{2})^{-8}=1^{-8}=1^8=1
h)
0,005^{-7}*2000^{-7}=(0,005*2000)^{-7}=10^{-7}=\frac{1}{10000000}=0,0000001
i)
5^{-2}:(-5)^{-2}=(\frac{5}{-5})^{-2}=(\frac{1}{-1})^{-2}=(\frac{-1}{1})^2=(-1)^2=1
j)
(\frac{1}{3})^{-4}:(1\frac{1}{3})^{-4}=(\frac{1}{3}:\frac{4}{3})^{-4}=(\frac{1}{\not3^1}*\frac{\not3^1}{4})^{-4}=(\frac{1}{4})^{-4}=4^4=256
k)
100^{-1}:0,1^{-1}=(\frac{100}{0,1})^{-1}=(\frac{1000}{1})^{-1}=\frac{1}{1000}=0,001
l)
60^{-7}:30^{-7}=(60:30)^{-7}=2^{-7}=(\frac{1}{2})^7=\frac{1}{128}
m)
24^{-6}:18^{-6}=(\frac{24}{18})^{-6}=(\frac{4}{3})^{-6}=(\frac{3}{4})^6=\frac{81}{256}
n)
(-16)^{-3}:(-8)^{-3}=(\frac{-16}{-8})^{-3}=(\frac{2}{1})^{-3}=(\frac{1}{2})^3=\frac{1}{8}
o)
0,6^5:6^5=(0,1)^5=(\frac{1}{10})^5=\frac{1}{100000}=0,00001
p)
2,5^{-1}:(\frac{5}{8})^{-1}=(\frac{25}{10}:\frac{5}{8}){-1}=(\frac{\not5^1}{\not2^1}*\frac{\not8^4}{\not5^1})^{-1}=(\frac{4}{1})^{-1}=\frac{1}{4}