Răspuns :
[tex]a)~21^{21}=21*21^{20}=[/tex]
[tex]=(25-4)*(21^{10})^{2}=[/tex]
[tex]=5^{2}*(21^{10})^{2}-2^{2}*(21^{10})^{2}[/tex]
[tex]=(5*21^{10})^{2}-(2*21^{10})^{2}[/tex]
[tex]b)~53^{53}=53*53^{52}=[/tex]
[tex]=(64-9)*(53^{26})^{2}=[/tex]
[tex]=8^{2}*(53^{26})^{2}-3^{2}*(53^{26})^{2}=[/tex]
[tex]=(8*53^{26})^{2}-(3*53^{26})^{2}[/tex]
[tex]c)~9^{99}=9*9^{98}=[/tex]
[tex]=(25-16)*(9^{49})^{2}=[/tex]
[tex]=5^{2}*(9^{49})^{2}-4^{2}*(9^{49})^{2}=[/tex]
[tex]=(5*9^{49})^{2}-(4*9^{49})^{2}[/tex]
[tex]d)~55^{55}=55*55^{54}=[/tex]
[tex]=(64-9)*(55^{27})^{2}=[/tex]
[tex]=8^{2}*(55^{27})^{2}-3^{2}*(55^{27})^{2}=[/tex]
[tex]=(8*55^{27})^{2}-(3*55^{27})^{2}[/tex]
[tex]e)~65^{65}=65*65^{64}=[/tex]
[tex]=(81-16)*(65^{32})^{2}=[/tex]
[tex]=9^{2}*(65^{32})^{2}-4^{2}*(65^{32})^{2}=[/tex]
[tex]=(9*65^{32})^{2}-(4*65^{32})^{2}[/tex]
[tex]f)~32^{31}=32*32^{30}=[/tex]
[tex]=(36-4)*(32^{15})^{2}=[/tex]
[tex]=6^{2}*(32^{15})^{2}-2^{2}*(32^{15})^{2}=[/tex]
[tex]=(6*32^{15})^{2}-(2*32^{15})^{2}[/tex]
[tex]=(25-4)*(21^{10})^{2}=[/tex]
[tex]=5^{2}*(21^{10})^{2}-2^{2}*(21^{10})^{2}[/tex]
[tex]=(5*21^{10})^{2}-(2*21^{10})^{2}[/tex]
[tex]b)~53^{53}=53*53^{52}=[/tex]
[tex]=(64-9)*(53^{26})^{2}=[/tex]
[tex]=8^{2}*(53^{26})^{2}-3^{2}*(53^{26})^{2}=[/tex]
[tex]=(8*53^{26})^{2}-(3*53^{26})^{2}[/tex]
[tex]c)~9^{99}=9*9^{98}=[/tex]
[tex]=(25-16)*(9^{49})^{2}=[/tex]
[tex]=5^{2}*(9^{49})^{2}-4^{2}*(9^{49})^{2}=[/tex]
[tex]=(5*9^{49})^{2}-(4*9^{49})^{2}[/tex]
[tex]d)~55^{55}=55*55^{54}=[/tex]
[tex]=(64-9)*(55^{27})^{2}=[/tex]
[tex]=8^{2}*(55^{27})^{2}-3^{2}*(55^{27})^{2}=[/tex]
[tex]=(8*55^{27})^{2}-(3*55^{27})^{2}[/tex]
[tex]e)~65^{65}=65*65^{64}=[/tex]
[tex]=(81-16)*(65^{32})^{2}=[/tex]
[tex]=9^{2}*(65^{32})^{2}-4^{2}*(65^{32})^{2}=[/tex]
[tex]=(9*65^{32})^{2}-(4*65^{32})^{2}[/tex]
[tex]f)~32^{31}=32*32^{30}=[/tex]
[tex]=(36-4)*(32^{15})^{2}=[/tex]
[tex]=6^{2}*(32^{15})^{2}-2^{2}*(32^{15})^{2}=[/tex]
[tex]=(6*32^{15})^{2}-(2*32^{15})^{2}[/tex]
