Question

Oblicz.
1. (25^3 * 81^2) : 15^6
2. (18^-1 - 12^-2) * 36^2
3. 6^4 * (8^0 - 4)^-4

Answer 1

1. (25^3 * 81^2) : 15^6  =
(5^2)^3 * (3^4)^2  : 5^6 * 3^6 =
5^6 *3^8 : 5^6 * 3^6 =
5^0 * 3^3 = 1 * 27 = 27

2. (18^-1 - 12^-2) * 36^2 =
18^-1 * 36^2 - 36^2 * 12^-2 =
18^-1 * 18^2 * 2^2 - 3^2 * 12^2 * 12^-2=
18^1 * 4 - 6 * 12^0 =
72 - 6 * 1 = 66

3. 6^4 * (8^0 - 4)^-4 =
6^4 * [1 - 4]^-4 =
6^4 * -3^-4 =
2^4 * 3^4 *3^-4 * -1^-4 =
2^4 * 3^0 * -1^-4 =
16 * 1 * 1 = 16