1)а)

81^6:243^4*27^6:9^6=(3^4)^6:(3^5)^4*(3^3)^6:(3^2)^6=3^24:3^20*3^18:3^12=3^24-20+18-12=3^10

б)2^3n-1*4^n+2:8^n-3=

2^3n-1*2^(n+2)*2:2^(n-3)*3

2^3n-1*2^2n+4:2^3n-9=2^3n-1+2n+4-3n+9=2^2n+12

3)

a)

9^7x+1=81^2x+4

9^7x+1=9^(2x+4)*2

9^7x+1=9^4x+8

7x+1=4x+8

3х=7

х=7/3

Х=2 1/3

Б)(4/9)^х+2=(16/81)^2х-5

(4/9)^х+2=(4/9)^(2х-5)*2

(4/9)^х+2=(4/9)^4х-10

х+2=4х-10

-3х=-12

3х=12

х=4

2)а)

50^3

____________ =

(2^2)^3*(5^2)^3

50^3

____________ =

4^3*25^3

50^3

____________ =

100^3

(50/100)^3

(1/2)^3