1. a) 8+25 + 81 + 16 = 130
b) 3*4 + 5*27 - 2*16 =12 + 135 - 32 =115
2. a) 2^(21+23-31) = 2^13
b) 3^18 : 3^6 *(3^2)^3 = 3^(18-6) * 3^6 = 3^12 * 3^6 = 3^18
c) ((2^3)^14 * 5^14):2^42 + 5^9 : (5^2)^3 - (5^2)^6 * 5^2 =
(2^42 * 5^14) : 2^42 + 5^9 : 5^6 - 5^12 * 5^2 =
5^14 + 5^3 - 5^14 = 5^3 = 125
3. a) 2^20(2*3^5 -5 + 2^2 * 3^2) =
2^20(2*243 - 5 + 4*9) =
2^20(486 - 5+ 36) = 2^20 * 517
b) 3^19(3^2 - 3 -1 ): ((3^2)^8 *5) =
3^19(9-4) : (3^16 *5) =
3^19*5 : 3^16 * 5 =
5(3^19 : 3^16) =
5* 3^3 = 5* 27 = 135
c) [2^12(2^4 -2-1)]^2 : [2^11(2^3+2^2+1)]^2 =
[2^12(16 -3)]^2 : [2^11(8+4+1)]^2 =
[2^12 * 13]^2 : [2^11 * 13]^2 =
[2^24 * 169] : [2^22 * 169] = 2^24 : 2^22 = 2^2 = 4
4. a) (2^x)^3 = 2^6
2^3x = 2^6
3x = 6 => x = 2
b) 3^(x-2) = 3^5
x-2 = 5 => x = 7
c) 5^(3x-2) = 5^4
3x-2 = 4
3x =6
x = 2
5. nu stiu
