Question

determinați ultima cifra a numarului a daca:
a=101^25+15^32-6^46​

Answer 1

 

$\displaystyle\bf\\Enunt:\\Determinati~ultima~cifra~a~numarului~a~daca:\\a=101^{25}+15^{32}-6^{46}\\\\Explicatii:\\Un~numar~cara~are~ultima~cifra~1~sau~5~sau~6\\la~orice~putere~ar~fi~ridicat, ultima~cifra~a~puterii~va~fi~aceeasi.\\\\Exempe:\\\\(1)\\11^2=121\\\\11^3=1331\\\\(5)\\25^2=625\\\\(6)\\16^2=256$

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$\displaystyle\bf\\Rezolvare:\\\\U(a)=U\left(U\Big(101^{25}\Big)+U\Big(15^{32}\Big)-U\Big(6^{46}\Big)\right)\\\\U(a)=U\left(U\Big(1^{25}\Big)+U\Big(5^{32}\Big)-U\Big(6^{46}\Big)\right)\\\\U(a)=U\Big(1+5-6\Big)\right)\\\\\boxed{\bf U(a)=0}$