+)

Vậy 145 = 5. 29

+)

Vậy 310 = 2. 5. 31 

+)

Vậy 2 020 = 22.5.101

a)A=62.93=6.6.9.9.9=2.3.2.3.3.3.3.3.3.3=22.38b)B=3.82.25=3.(2.2.2).(2.2.2).5.5=26.3.52

\(=>x\in\left\{15;20;25;30;35;40;45;50;55;60;65;70;75\right\}\)

x⋮5 ⇒x tận cùng là 0 hoặc 5

mà 13<x≤78 ⇒xϵ(15,20,25...75)

Cmr: A =  27²⁷ + 3⁷⁷ ⋮ 82

        A =   (3³)²⁷ + 3⁷⁷

         A =  3⁸¹ + 3⁷⁷

        A = 3⁷⁷.( 3⁴ + 1)

       A  = 3⁷⁷. 82

        vì  82 ⋮ 82 ⇔ 3⁷⁷.82 ⋮ 82 ⇔ A = 27²⁷ + 3⁷⁷ ⋮ 82 (đpcm)

\(A=27^{27}+3^{77}⋮82\)

\(A=\left(3^3\right)^{27}+3^{77}⋮82\)

   { 15 + 2.[ 8- (5-3)]} : 9

= { 15 + 2. [ 8- 2]} : 9

= { 15 + 2.6}: 9

= {15 + 12}: 9

= 27 : 9

= 3 

\(9^7.9=9^{7+1}=9^8\\ x.x^3.x^4=x^{1+3+4}=x^8\)

a) 420 = 2² . 3 . 5 . 7

b) 840 = 2³ . 3 . 5 . 7

c) 225 = 3² . 5²

d) 128 = 2⁷

e) 252 = 2² . 3² . 7

a, (x-1)(x+1)  = 15

       x² - 1  = 15

             x² =  15 + 1

             x² =  16

             x    = +- 4 

   b,   xy + x + 2y  = 8

 (xy+x)  + 2y  + 2  = 10

 x.(y+1) + 2(y + 1) = 10

          (y+1)(x+2)  =  10

th1: y + 1 = 1; x + 2 = 10 ⇔ y = 0; x = 8

th2: y+ 1 = -1 ; x + 2 = -10 ⇔ y = -2; x  = -12

th3 : y + 1 = -2;  x + 2 = - 5 ⇔ y = -3; x = -7

th4: y + 1 = 2; x + 2 = 5 ⇔ y = 1; x = 3

th5: y + 1 = 5; x + 2  = 2 ⇔ y = 4;  x = 0

th6: y + 1 = -5 ;  x + 2 = -2 ⇔ y = -6; x = -4

th7: y + 1 = 10;  x + 2 = 1 ⇔ y = 9; x = -1

th8: y + 1 = -10 ; x + 2 = -1 ⇔ y = -11; x= -3

vậy (x,y) =( 8 ;0); (-12; -2); (-7; -3); (3; 1); ( 0;4); (-4;6); (-1;9);(-3;-11)

c, xy - 2x = 7

    x.(y-2) = 7

th1: x = 7; y-2 = 1 ⇔ x =7; y= 3

th2: x = -7; y-2 = -1 ⇔ x= -7; y = 1

th3  x = 1 ; y-2 = 7 ⇔ x = 1; y= 9

th4: x =- 1;  y-2 = -7 ⇔ x = -1; y = -5

vậy (x,y) =( -7;1); (1; 9) ; ( -1; -5)