1zad.
2 * 5²⁰-5¹⁸
------------- =
25⁹
5¹⁸ *(2 * 5² - 1)
-------------------- =
(5²)⁹
5¹⁸ *(2 * 5² - 1)
-------------------- =
5¹⁸
2 * 5² - 1 = 2 * 25 - 1 = 50 - 1 = 49
2zad.
(2¹⁹+2¹⁸) * 3²
------------------- =
(2¹⁸+2¹⁷) * 27
(2¹⁷⁺²+2¹⁷⁺¹) * 9
------------------------- =
(2¹⁷⁺¹ + 2¹⁷) * 27
2¹⁷ * (2²+2¹)
----------------------- =
2¹⁷ * (2¹+1) * 3
2²+2¹
-----------------=
(2¹+1) * 3
4+2
-----------=
3 * 3
6/9 = 2/3
3zad.
[(1½)⁻¹-3⁻²]⁻² = [(3/2)⁻¹-3⁻²]⁻² = [(2/3) -3⁻²]⁻² =
[(2/3) -(1/9)]⁻² = [(6/9) -(1/9)]⁻² = [5/9]⁻² = 81/25
4zad.
1⁻¹+2⁻¹+3⁻¹
------------------- =
(¾)⁻¹+3⁻¹*2
1+1/2+1/3
------------------- =
(4/3)+(1/3) *2
6/6+3/6+2/6
------------------- =
(4/3)+(2/3)
11/6
------- =
6/3
11/6
------- = 11/12
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