Question

Rezolva urmatoarele exercitii: MULTUMESC ANTICIPAT!!!! =D
1) 1+2+3+...+72=......
2) 53+368 : (1463:7-1608:8) +1=...
3) 336: ( 7 la puterea a2a + 0 la puterea a7a - 5 la puterea a2a) =
4) b la puterea a13a x (ori) b x (ori) b la puterea 21 x (ori) b la puterea 20=
5) 16 la puterea a4a x 4 la puterea 10 x 64 la puterea a5a =.....
6) c la puterea 58 : c la puterea 39 : c la puterea 9
7) 125 la puterea 42 : 25 la puterea 63=
8) (8 la puterea 37 x 81 la puterea 25) : (16 la puterea 27 x 27 la puterea 33) =
9) 2 la puterea 1 x 2 la puterea a2a x 2 la puterea a3a x 2 la puterea 4 x ... x 2 la puterea 45
10) 12- ( x+1) =2,4 aici x = numar natural

Answer 1

1.) 72*73/2=2628, Am folosit regula lui Gauss: $\frac{n(n+1)}{2}$.
2.) 53+368:(209-201)+1=53+368:8+1=53+46+1=100
3.) 336:(49+0-25)=336:24=14
4.) ⇒$b^{13+1+21+20} = b^{55}$
5.) 16=$2^{4}$, 4=2², 64=$2^{6}$
$2^{16} * 2^{20} *2^{30} = 2^{66}$
6.) $c^{58-39-9} = c^{10}$
7.) $5^{3*42} : 5^{2*63} = 5^{126} : 5^{126} =1$
8.) $2^{3*37} * 3^{4*25} : 2^{4*27} * 3^{3*33} = 2^{111} * 3^{100} : 2^{108} * 3^{99} =$= 2³*3=24
9.) Se face regula lui Gauss pt puteri: 45*46/2=1035
⇒S=$2^{1035}$
10.) x+1=12-2,4⇒x+1=9,6⇒x=9,6-1⇒x=8,6.

Answer 2

$1).1+2+3+...+72=72(72+1):2=(72*73):2= \\ =5256:2=2628 \\ 2).53+368:(1463:7-1608:8)+1=53+368:(209-201)+1= \\ =53+368:8+1=53+46+1=99+1=100 \\ 3).336:(7^2+0^7-5^2)=336:(49+0-25)=336:24=14 \\ 4).b^1^3*b*b^2^1*b^2^0=b^1^3^+^1^+^2^1^+^2^0=b^5^5$
$5).16^4*4^1^0*64^5=(4^2)^4*4^1^0*(4^3)^5=4^8*4^1^0*4^1^5= \\ =4^8^+^1^0^+^1^5=4^3^3 \\ 6).c^5^8:c^3^9:c^9=c^5^8^-^3^9^-^9=c^1^0 \\ 7).125^4^2:25^6^3=(5^3)^4^2:(5^2)^6^3=5^1^2^6:5^1^2^6=5^1^2^6^-^1^2^6=5^0=1 \\ 8).(8^3^7*81^2^5):(16^2^7*27^3^3)=[(2^3)^3^7*(3^4)^2^5]:[(4^2)^2^7*(3^3)^2^5]= \\ =(2^1^1^1*3^1^0^0):(2^1^0^8*3^9^9)=2^1^1^1^-^1^0^8*3^1^0^0^-^9^9=2^3*3=8*3=24$
$9).2^1*2^2*2^3*2^4*...*2^4^5=1+2+3+...+45= \\ =45(45+1):2=(45*46):2=2070:2=1035=2^1^0^3^5 \\ 10).12-(x+1)=2,4 \\ 12-x-1=2,4 \\ -x=2,4-12+1 \\ -x=-8,6 \\ x=8,6$