Question

d)7^5*7^6/7^10+5^4/5+4^2=
e)(3^8*5^3)^3:(3^5*5^2)^4=
f)(6^8*5^3)^3/(3^5*5^2)^4=
g)[5^17*(5^2)^3+7^23/(7^5)^3]/[7*7^2*7^5+5^2^5/5^9]=
h)[7^17*(7^2)^3+3^23/(5^3)^5]/[3^2*3^2*3^3+7^2^5/7^9]=
j)3*[5^3^2/5^2^3+(3^4-2^4*5)^2015+8^7/16^5=

e)(2^7*3^5)^2=
f)(3^2*5^3)^3/(3*5^2)^4=
g)(2^5*7^3)^2/(2^3*7^2)^3=
h)2^3+[(2^3)^7-(2^7)^3]*2*2^2013=
j){2^0+2*2^3*2^5+[(2^3)^2]^6}/(+16*2^5+2^36)=
k)3^5/9^2+5^4*25^2/125^3-2^6/4^3=

Aflati cel mai mic numar natural de 4 cifre care impartit la 23 da restul 15.
Aflati cel mai mare numar natural de trei cifre care impartiti la 12 da restul 5.
Aflati cel mai mic numar natural care impartit la 320 da rest un numar impar, iar catul este 83.
Aflati ce numar natural impartit la 27 da catul 35 si restul 14.
Aflati toate numerele naturale care impartite la 4 dau catul 24.
Aflati toate numerele naturale care impartite la 6 dau catul 32.

Answer 1

d)7^11/7^10+5^4/5+4^2=
=7+125+16=148

e)(3^8*5^3)^3:(3^5*5^2)^4=
=(3^24*5^9):(3^20*5^8)=
=3^4*5=81*5=405

f)(6^8*5^3)^3/(3^5*5^2)^4=
=(2^8*3^8*5^3)^3/(3^5*5^2)^4=
=(2^24*3^24*5^9)/(3^20*5^8)=
=2^24*3^4*5=6794772480


 g)[5^17*(5^2)^3+7^23/(7^5)^3]/[7*7^2*7^5+5^2^5/5^9]=
=[5^17*5^6+7^23/(7^15)]/[7*7^7+5^32/5^9]=
=[5^23+7^8]/[7^8+5^23]=1

 h)[7^17*(7^2)^3+3^23/(3^3)^5]/[3^3*3^2*3^3+7^2^5/7^9]=
=[7^23+3^23/3^15]/[3^8+7^32/7^9]=
=[7^23+3^8]/[3^8+7^23]=1

j)3*[5^3^2/5^2^3+(3^4-2^4*5)^2015+8^7/16^5]=
=3*[5^9/5^8+(81-80)^2015+2^21/2^20]=
=3*[5+1^2015+2]=
=3*[5+1+2]=
=3*8=24

 e)(2^7*3^5)^2=2^14*3^10
f)(3^2*5^3)^3/(3*5^2)^4=
=(3^6*5^9)/(3^4*5^8)=
=3^2 *5=9*5=45

g)(2^5*7^3)^2/(2^3*7^2)^3=
=(2^10*7^6)/(2^9*7^6)=
=2

 h)2^3+[(2^3)^7-(2^7)^3]*2*2^2013=
=2^3+[(2^21-2^21]*2*2^2013=
=2^3+0*2*2^2013=2^3=8

 j){2^0+2*2^3*2^5+[(2^3)^2]^6}/(1+16*2^5+2^36)=
={1+2^9+(2^36]/(1+2^9+2^36)=1     
(aici am facut ceva modificari-verifica)

 k)3^5/9^2+5^4*25^2/125^3-2^6/4^3=
=3^5/3^4+5^4*5^4/5^9-2^6/2^6=
=3+5^8/5^9-1=
=2+1/5=
=11/5
 Aflati cel mai mic numar natural de 4 cifre care impartit la 23 da restul 15.
1000:23≈43,47
23*43+15=1004
Aflati cel mai mare numar natural de trei cifre care impartiti la 12 da restul 5.
100:12≈8,333
12*8+5=101
Aflati cel mai mic numar natural care impartit la 320 da rest un numar impar, iar catul este 83.
x:320=83  si rest nr impar
83*320+1=26561
Aflati ce numar natural impartit la 27 da catul 35 si restul 14.
x:27=35 si rest 14
x=27*35+14=959
Aflati toate numerele naturale care impartite la 4 dau catul 24.
4*24=96
4*24+1=97
4*24+2=98
4*24+3=99
Aflati toate numerele naturale care impartite la 6 dau catul 32.
6*32=192
6*32+1=193
6*32+2=194
6*32+3=195
6*32+4=196
6*32+5=197