Răspuns :
[tex]1a).(25^4)^3:(4^2+3^2)^1^1-(0^2^0^1^0+1^2^0^1^2+2013^0)= \\ =25^1^2:(16+9)^1^1-(0+1+1)=25^1^2:25^1^1-2= \\ =25^1^2^-^1^1-2=25^1-2=25-2=23[/tex]
[tex]b).[123+2^7*2^2+2^6^7:2^2^7]:[123+2^1^4:2^5+(2^5)^8]= \\ =(123+2^7^+^2^+^6^7^-^2^7):(123+2^1^4^-^5+2^4^0)= \\ =(123+2^4^9):(123+2^9+2^4^0)=(123+2^4^9):(123+2^9^+^4^0)= \\ =(123+2^4^9):(123+2^4^9)=1[/tex]
[tex]c).(2^8+9^2+5^6+36^2):(0^6+4^4+3^4+25^3+6^4)= \\ =[2^8+(3^2)^2+5^6+(6^2)^2]:[0+(2^2)^4+3^4+(5^2)^3+6^4]= \\ =(2^8+3^4+5^6+6^4):(2^8+3^4+5^6+6^4)=1[/tex]
[tex]d).(4+8+12+16+...+8000):(2+4+6+8+....+4000)+ \\ +(2^5^3+2^5^2+2^5^1):(2^1^7)^3 \\ 4+8+13+16+...+8000=4(1+2+3+...+2000) \\ 2+4+6+8+...+4000=2(1+2+3+...+2000) \\ 4(1+2+3+...+2000):2(1+2+3+...+2000)=2 \\ (2^5^3+2^5^2+2^5^1):(2^1^7)^3=2^5^1(2^2+2+1):2^5^1= \\ =2^5^1(4+2+1):2^5^1=4+2+1=7 \\ 2+7=9[/tex]
e).{637+15*[15*(282:47+516:43):45-6]:21}:13=
={637+15*[15*(6+12):45-6]:21}:13=
=[637+15*(15*18:45-6):21]:13=
=[637+15*(270:45-6):21]:13=
=[637+15*(6-6):21]:13=
=(637+15*0:21):13=
=637:13=
=49
[tex]f).(6+12+18+24+...+600)^2:(3+6+9+12+...+300): \\ :(1+2+3+...+100) \\ (6+12+18+24+...+600)^2=[6(1+2+3+...+100)]^2= \\ = 36(1+2+3+...+100)^2= \\ =36(1+2+3+...+100)(1+2+3+...+100) \\ 3+6+9+12+...+300=3(1+2+3+...+100) \\ 36:3=12[/tex]
[tex]2a).a=[a^5+a^7+(a^1)^2^0]^0:[(a^2)^4:(a^4)^2] \\ a=1:(a^8:a^8) \\ a=1:1 \\ a=1 [/tex]
[tex]b).b=[(2^3)^5+25^3-7^3^5:7^2^0]:(2^1^5-7^1^5+5^6)*3^3^6 \\ b=[2^1^5+(5^2)^3-7^3^5^-^2^0]:(2^1^5-7^1^5+5^6)*3^3^6 \\ b=(2^1^5+5^6-7^1^5):(2^1^5-7^1^5+5^ 6)*3^3^6 \\ b=3^3^6[/tex]
[tex]c).[2+2^2*2^2^2+2^2^0^0:2^1^2^0+(3^3)^1^0]:[1+2^2^4+2^8^0+2^2^0^1^ 3+3^3^0]- \\ -2+(5^7)^3 \\ c=(2+2^2^4+2^8^0+3^3^0):(1+2^2^4+2^8^0+2^2^0^1^3+3^3^0)-2+5^2^1 \\ c=1-2+5^2^1 \\ c=5^2^1-1[/tex]
[tex]b).[123+2^7*2^2+2^6^7:2^2^7]:[123+2^1^4:2^5+(2^5)^8]= \\ =(123+2^7^+^2^+^6^7^-^2^7):(123+2^1^4^-^5+2^4^0)= \\ =(123+2^4^9):(123+2^9+2^4^0)=(123+2^4^9):(123+2^9^+^4^0)= \\ =(123+2^4^9):(123+2^4^9)=1[/tex]
[tex]c).(2^8+9^2+5^6+36^2):(0^6+4^4+3^4+25^3+6^4)= \\ =[2^8+(3^2)^2+5^6+(6^2)^2]:[0+(2^2)^4+3^4+(5^2)^3+6^4]= \\ =(2^8+3^4+5^6+6^4):(2^8+3^4+5^6+6^4)=1[/tex]
[tex]d).(4+8+12+16+...+8000):(2+4+6+8+....+4000)+ \\ +(2^5^3+2^5^2+2^5^1):(2^1^7)^3 \\ 4+8+13+16+...+8000=4(1+2+3+...+2000) \\ 2+4+6+8+...+4000=2(1+2+3+...+2000) \\ 4(1+2+3+...+2000):2(1+2+3+...+2000)=2 \\ (2^5^3+2^5^2+2^5^1):(2^1^7)^3=2^5^1(2^2+2+1):2^5^1= \\ =2^5^1(4+2+1):2^5^1=4+2+1=7 \\ 2+7=9[/tex]
e).{637+15*[15*(282:47+516:43):45-6]:21}:13=
={637+15*[15*(6+12):45-6]:21}:13=
=[637+15*(15*18:45-6):21]:13=
=[637+15*(270:45-6):21]:13=
=[637+15*(6-6):21]:13=
=(637+15*0:21):13=
=637:13=
=49
[tex]f).(6+12+18+24+...+600)^2:(3+6+9+12+...+300): \\ :(1+2+3+...+100) \\ (6+12+18+24+...+600)^2=[6(1+2+3+...+100)]^2= \\ = 36(1+2+3+...+100)^2= \\ =36(1+2+3+...+100)(1+2+3+...+100) \\ 3+6+9+12+...+300=3(1+2+3+...+100) \\ 36:3=12[/tex]
[tex]2a).a=[a^5+a^7+(a^1)^2^0]^0:[(a^2)^4:(a^4)^2] \\ a=1:(a^8:a^8) \\ a=1:1 \\ a=1 [/tex]
[tex]b).b=[(2^3)^5+25^3-7^3^5:7^2^0]:(2^1^5-7^1^5+5^6)*3^3^6 \\ b=[2^1^5+(5^2)^3-7^3^5^-^2^0]:(2^1^5-7^1^5+5^6)*3^3^6 \\ b=(2^1^5+5^6-7^1^5):(2^1^5-7^1^5+5^ 6)*3^3^6 \\ b=3^3^6[/tex]
[tex]c).[2+2^2*2^2^2+2^2^0^0:2^1^2^0+(3^3)^1^0]:[1+2^2^4+2^8^0+2^2^0^1^ 3+3^3^0]- \\ -2+(5^7)^3 \\ c=(2+2^2^4+2^8^0+3^3^0):(1+2^2^4+2^8^0+2^2^0^1^3+3^3^0)-2+5^2^1 \\ c=1-2+5^2^1 \\ c=5^2^1-1[/tex]
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