1.
(-3)^3 = -27
-6^0 = 1
(-1,3)^2 = 1,69
-0,1^4 = -0,0001
-(-0,4)^3 = -(-0,064) = 0,064
2.
(2/5)^2 -( -2/5)^3 = 4/25 - (-8/125) = 4/25 + 8/125 = 20/125 + 8/125 = 28/125
(3/7)^2 - 3^3/7 + 3/7^2 = 9/49 - 9/7 + 3/49 = 9/49 -63/49 + 3/49 = -51/49
30*(-0,1)^3 - 0,1 * 30^3 = 30* (-0,001) - 0,1 * 27000 = -0,03 - 2700 = -2700,03
10^2 * 1/10 -(-1/10)^0 *(-10) = 100 * 1/10 -(-1) * (-10) = 10 + 1 *(-10) = 10-10 = 0
3.
8*2^3 * 2^5 = 2^3 * 2^3 * 2^5 = 2^11
81*3^5:3^3 = 3^4 * 3^5:3^3 = 3^9 : 3^3 = 3^6
64*16:2^6 = 2^6 * 2^4 : 2^6 = 2^4
4.
5^10 : 5^7 = 5^3
3^8 : 243 = 3^8:3^5 = 3^3
2^12: 64*4^2 = 2^12 : 2^6 * 2^4 = 2^12 : 2*10 = 2^2
5.
(5^3)^5 = 5^15
125^6 = (5^3)^6 = 5^18
5^3^2 = 125^2 = (5^3)^2 = 5^6
5^2^3 = 25^3 = (5^2)^3 = 5^6
5^3^2 = 5^2^3 < (5^3)^5 < 125^6
6.
a = 2^9
b = 2^6:2^2 = 2^4
c = 2^4
(a-b)/c = (2^9 - 2^4)/2^4 = 2^4(2^5 - 1)/2^4 = 2^5 - 1
wynik bez potęg: 3125 - 1 = 3124
7.
5^7 * 2^7 = 10^7
10^7:17^3 = 10^4
10^4 * 0,8^4 = 8^4
8^4 : 16^4 = (2^3)^4 : (2^4)^4 = 2^12 : 2^16 = 2^-4
8.
2^9 * 5^7 = 2^2 * 2^7 * 5^7 = 2^2 * 10^7
0,2^6 * 5^3 = 0,2^3 * 0,2^3 * 5^3 = 0,2^3 * 1^3 = 0,2^3
(2/3)^6 : (4/9)^5 = (2/3)^6 : (2/3^2)^5 = (2/3)^6 : (2/3)^10 = (2/3)^-4
9.
((b^6)^3 * b)/(b^5)^2 = (b^18*b^1)/b^10 = b^19/b^10 = b^9
odp: C
10.
1% * 10^10 = 0,01 * 10^10 = 10^-2 * 10^10 = 10^8
10% * 10^18 = 0,1 * 10^18 = 10^-1 * 10^18 = 10^17
50% * 2^9 = 0,5*2^9 = 1/2 * 2^9 = 2^-1 + 2^9 = 2^8
25% * 2^30 = 1/4 * 2^30 = 2^-2 * 2^30 = 2^28
11.
1/3 * 27^6 = 3^-1 * (3^3)^6 = 3^-1 * 3^18 = 3^17
