Matematică
pawlon1995
5

Am nevoie de ajutor!Va rog,daca nu stiti nu raspundeti,nu e vorba ca nu e stiu face dar nu mai am timp!Va rog,ajutati-ma la aceste exercitii: 1.Calculati: a)(-8)^54*8^200-8^254= b)[(-6)^5]^201:(-6)^1004+34:(-17)= c)(-12)^93:(-12^8*12^5)^7-144= d)[3*3^2*3^3*...*3^100]:(-3)^5049. Atentie!Raspunsurile aiurea vor fi sterse,va rog,nu raspundeti daca nu stiti!

+0
(2) Răspunsuri
MarianCosmin2

a) [latex](-8)^{54}\cdot8^{200}-8^{254}=8^{54}\cdot8^{200}-8^{254}=8^{254}-8^{254}=0\\   b) [(-6)^5]^{201}=(-6)^{1005}= (-6)^{1005}\\ (-6)^{1005}:(-6)^{1005}=-6\\ 34:(-17)=-2\\ -6+(-2)=-8 [/latex] c)[latex](-12)^8=12^8\\ 12^8\cdot12^5=12^{13}\\ 12^{13}^7=12^{91} 12^{93}:12^{91}=12^2=144\\ 144-144=0 [/latex] d) [latex]3\cdot3^2\cdot3^3 ...\cdot3^{100}=3^{5050}  1+2+3+...+100= 5050 ~(suma ~Gauss)\\ (-3)^{5049}=(-1)\cdot3^{5049}\\ 3^{5050}:(-1)\cdot3^{5049}=-3 [/latex]

cmihai14

[latex]1a).(-8)^5^4 \cdot8^2^0^0-8^2^5^4=8^5^4^+^2^0^0-8^2^5^4= 8^2^5^4-8^2^5^4=0 \\ b).[(-6)^5]^2^0^1:(-6)^1^0^0^4+34:(-17)= (-6)^1^0^0^5:(-6)^1^0^0^4+(-2)= \\ =-6+(-2)=-8 \\ c).(-12)^9^3:(-12^8 \cdot 12^5)^7-144=(-12)^9^3:(12^8^+^5)^7-144= \\ =(-12)^9^3:(12^1^3)^7-144=(-12)^9^3:12^9^1-144= \\ =12^9^3^-^9^1-144=12^2-144=144-144=0[/latex] [latex]d).[3 \cdot 3^2 \cdot 3^3 \cdot ... \cdot3^1^0^0]:(-3)^5^0^4^9 \\ 1+2+3+...+100=100(100+1):2=(100 \cdot 101) :2= \\ =10100:2=5050 \\ 3^5^0^5^0:(-3)^5^0^4^9=-3^5^0^5^0^-^5^0^4^9=-3^1=-3[/latex]

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