Question

Ex nr 1.: Calculati:
1) (4/5)^13:[(4/5)^2]^6=.........
2) {[(2/3)^1007×(2/3)^3]^2×(2/3)^2000} ×(2/3)^4000=.......
3) 3:(2intregi si 3/4- 1intreg si 15/28)+2/3:3/2=...........
Ex nr 2.:Rezolvati ecuatiile in Q+:
1) 15x-6/4 - 3x/2=1
2) 6(3x-2)+5=17x-2
3) 2,(3)x+ 1intreg si 1/6=0,(6)x+ 2intregi 1/3

Answer 1

1.(4/5)¹³:(4/5)¹²=(4/5)¹³⁻¹²=(4/5)

{[(2/3)¹⁰⁰⁷·(2/3)³]²·(2/3)²⁰⁰⁰}·(2/3)⁴⁰⁰⁰=[(2/3)¹⁰¹⁰]²·(2/3)²⁰⁰⁰]·(2/3)⁴⁰⁰⁰=(2/3)²⁰²⁰·(2/3)²⁰⁰⁰·(2/3)⁴⁰⁰⁰=(2/3)⁸⁰²⁰

3:(11/4-43/28)+2/3·2/3=
3:(77-43)/28+4/9=
3·28/34+4/9=
84/34+4/9=
42/17+4/9=
(378+68)/153=446/153=2 intreg 140/153

2.
a)60x-6-6x=4
52x=10
x=10/52=5/26

b)18x-12+5=17x-2
x=5

c)2 intreg 3x/9+7/6=2x/3+7/3
7x/3+7/6=2x/3+7/3
14x+7=4x+14
10x=7
x=7/10