1/34 a) 9^2 = 9 * 9 = 81 9^3 = 9 * 9 * 9 = 729 9^4 = 9 * 9 * 9 * 9 = 5861 b) (3/4)^2 = 9/16 (3/4)^3 = 27/64 (3/4)^4 = 81/256 c) (-2/5)^2 = -4/25 (-2/5)^3 = -8/125 (-2/5)^4 = -16/625 3/35 a) 4^-2 = (1/4)^2 = 1/16 b) 4^-3 = (1/4)^3 = 1/64 c) (-3)^-2 = (-1/3)^2 = -1/9 d) (-3)^-3 = (-1/3)^3 = -1/27 e) (1/2)^-2 = 2^2 = 4 f) (1/2)^-5 = 2^5 = 32 g) (2/3)^-2 = (3/2)^2 = 9/4 = 2 1/4 h) (-2/3)^-4 = (-3/2)^4 = -81/16 = -5 1/16 i) (0,2)^-2 = (1/5)^-2 = 5^2 = 25 j) (-0,2)^-3 = (-1/5)^-3 = (-5)^3 = (-125) 1/36 a) (-2)^5 = -32 (-2)^-5 = (-1/2)^5 = -1/32 2^-5 = (1/2)^5 = 1/32 b) (1/3)^-2 = 3^2 = 9 (-1/3)^-2 = -3^2 = 9 (-1/3)^-3 = -3^3 = -27
Ćwiczenie 2 str. 34 (-3)^{9} < (-2)^{9} < (-2)^{4} < (-3)^{4} ćw.1 str, 34 a. [latex]9^{2}[/latex] = 81 9^{3} = 729 9^{4} = 6561 b. [latex](frac{3}{4})^{2} =frac{9}{16} [/latex] 3/4^{3}= 27/64 3/4^{4} = 81/384 c. (-2/5)^{2} = 4/25 (-2/5)^{3} = -8/125 (-2/5)^{4} = 16/625 Ćw. 3. str 35 w tym zadaniu stosuje się wzór, który masz podany w książce i myślę, że spokojnie jesteś w stanie zrobić to zadanie sam/sama. a. 4^{-2} = 1/4^{2} = 1/16 b. 4^{-3} = 1/4^{3} = 1/64 c. (-3)^{-2} = 1/(-3)^{2} = 1/9 itd. Zad.1. str. 36 a. -2^{5} = 32 -2^{-5} = 1/(-2)^{5} = 1/-32 = -1/32 2^-{5} = 1/32 b. 1/3^{-2} = 1/ (1/3)^{2} = 1/ (1/9) = 1 * 9 = 9 (-1/3)^{-2} = 9 (-1/3)^{-3} = 1/ (-1/3)^{3} = 1/ (-1/27) = -27 c. [latex](sqrt{3})^{4} = 3 * 3 = 9 (sqrt{3})^{-2} = 1/ (sqrt{3})^{2} = 1/3 (sqrt{3})^{-6} = 1/ (sqrt{3})^{6} = 1/729[/latex] d. [latex](sqrt{2})^{6} = 2 * 2 * 2 = 8 (sqrt{2})^{7} = 8sqrt{2} (sqrt{2})^{-8} = 1/ (sqrt{2})^{8} = 1/16[/latex]
