[tex]1 \ km = 1000 \ m = 10^{3} \ m\\1 \ m = 100 \ cm = 10^{2} \ cm\\1 \ cm = 10 \ mm[/tex]
Z własności potęg:
[tex](a\cdot b)^{n} = a^{n}\cdot b^{n}\\(a^{n})^{m} = a^{m\cdot m}[/tex]
a)
[tex]1 \ km^{2} = (10^{3} \ m)^{2} = (10^{3})^{2} \ m^{2} = 10\boxed{^{6}} \ m^{2}\\\\100 \ km^{2}=100\cdot10^{6} \ m^{2} = 10^{2}\cdot10^{6} \ m^{2} = 10\boxed{^{8}} \ m^{2}[/tex]
b)
[tex]1 \ m^{2} = (100 \ cm)^{2} = (10^{2})^{2} \ cm^{2} = 10\boxed{^{4}} \ cm^{2}\\\\10^{5} \ m^{2} = 10^{5}\cdot10^{4} \ cm^{2} = 10\boxed{^{9}} \ cm^{2}[/tex]
c)
[tex]1 \ cm^{2} = (10 \ mm)^{2} = 10\boxed{^{2}} \ mm^{2}\\\\10 \ cm^{2} = 10\cdot10^{2} \ mm^{2} = 10\boxed{^{3}} \ mm^{2}[/tex]
d)
[tex]1 \ km^{2} = (10^{5} \ cm)^{2} = (10^{5})^{2} \ cm^{2} = 10\boxed{^{10}} \ cm^{2}[/tex]
[tex]10 \ km^{2} = 10\cdot10^{11} \ cm^{2} = 10\boxed{^{11}} \ cm^{2}[/tex]
