`1)`
`C_1 : A = {11 ; 12 ; 13 ; 14 ; 15}`
`C_2 : A = {x ∈ N | 10 < x ≤ 15}`
`10 ∉ A` `15 ∈ A` `13 ∈ A` `16 ∉ A`
`2)`
`a) 3^3 . 3^2 = 3^5 = 243`
`b) 6^9 : 6^8 = 6^1 = 6`
`c) 4^3 : 4 = 4^3 : 4^1 = 4^2 = 16`
`d) 16 . 2^3 = 2^4 . 2^3 = 2^7 = 128`
`3)`
`a) (x - 17) + 61 = 75`
`x - 17 = 75 - 61`
`x - 17 = 14`
`x = 14 + 17`
`x = 31`
`b) 420 - 2x = 120`
`2x = 420 - 120`
`2x = 300`
`x = 300 : 2`
`x = 150`
`c) 12 + 8(13 - x) = 52`
`8(13 - x) = 52 - 12`
`8(13 - x) = 40`
`13 - x = 40 : 8`
`13 - x = 5`
`x = 13 - 5`
`x = 8`
`d) (12x - 140) . 5^5 = 4. 5^7`
`(12x - 140) . 3125 = 4. 78125`
`(12x - 140) . 3125 = 312500`
`12x - 140 = 312500 : 3125`
`12x - 140 = 100`
`12x = 100 + 140`
`12x = 240`
`x = 240 : 12`
`x = 20`
`e) x^10 = x`
`=> x = 0 ; 1`
`f) 2^x : 8 = 4`
`2^x = 4 . 8`
`2^x = 32`
`=> x = 5`
`4)`
`a)12 . 3^2 - 24 . 2^2`
`= 12. 9 - 24 . 4`
`= 108 - 96`
`= 12`
`b) 100 - [35 + (13 - 5)^2]`
`= 100 - (35 + 8^2)`
`= 100 - (35 + 64)`
`= 100 - 99`
`= 1`
`c) 96 - 96 : [12 + 4(3^0 + 2^3)]`
`=96 - 96 : [12 + 4(1 + 8)`
`= 96 - 96 : [12 + 4 . 9)`
`= 96 - 96 : (12 + 36)`
`= 96 - 96 : 48`
`= 96 - 2`
`= 94`
`d) 2^3 . 2^2 - (45 - 40)^2`
`= 2^5 - 5^2`
`= 32 - 25`
`= 7`
`e) (8^2016 - 8^2014) : 8^2014`
`= 8^2016 : 8^2014 - 8^2014 : 8^2014`
`= 8^2 - 8^0`
`= 64 - 1`
`= 63`
