miniaufgabe.js
==== 14. November 2022 bis 18. November 2022 ====
=== Dienstag 15. November 2022 ===
Prüfung, keine Miniaufgabe
=== Donnerstag 17. November 2022 ===
Resultat als Bruch von Potenzen mit positiven Exponenten von Primzahlen.miniAufgabe("#exonegex_numberpower","#solnegex_numberpower",
[["$\\displaystyle \\frac{12^{-2}}{18^{-4}}$", "$\\displaystyle \\frac{12^{-2}}{18^{-4}} = \\frac{\\left(2^{2} \\cdot 3\\right)^{-2}}{\\left(2 \\cdot 3^{2}\\right)^{-4}} = \\frac{\\left(2 \\cdot 3^{2}\\right)^{4}}{\\left(2^{2} \\cdot 3\\right)^{2}} = \\frac{2^{4} \\cdot 3^{8}}{2^{4} \\cdot 3^{2}} = 3^{6}$"], ["$\\displaystyle \\frac{28^{-2}}{98^{-3}}$", "$\\displaystyle \\frac{28^{-2}}{98^{-3}} = \\frac{\\left(2^{2} \\cdot 7\\right)^{-2}}{\\left(2 \\cdot 7^{2}\\right)^{-3}} = \\frac{\\left(2 \\cdot 7^{2}\\right)^{3}}{\\left(2^{2} \\cdot 7\\right)^{2}} = \\frac{2^{3} \\cdot 7^{6}}{2^{4} \\cdot 7^{2}} = \\frac{7^{4}}{2}$"], ["$\\displaystyle \\frac{175^{-3}}{245^{-4}}$", "$\\displaystyle \\frac{175^{-3}}{245^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{-3}}{\\left(5 \\cdot 7^{2}\\right)^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{4}}{\\left(5^{2} \\cdot 7\\right)^{3}} = \\frac{5^{4} \\cdot 7^{8}}{5^{6} \\cdot 7^{3}} = \\frac{7^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{28^{-2}}{98^{-4}}$", "$\\displaystyle \\frac{28^{-2}}{98^{-4}} = \\frac{\\left(2^{2} \\cdot 7\\right)^{-2}}{\\left(2 \\cdot 7^{2}\\right)^{-4}} = \\frac{\\left(2 \\cdot 7^{2}\\right)^{4}}{\\left(2^{2} \\cdot 7\\right)^{2}} = \\frac{2^{4} \\cdot 7^{8}}{2^{4} \\cdot 7^{2}} = 7^{6}$"], ["$\\displaystyle \\frac{75^{-3}}{45^{-4}}$", "$\\displaystyle \\frac{75^{-3}}{45^{-4}} = \\frac{\\left(3 \\cdot 5^{2}\\right)^{-3}}{\\left(3^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(3^{2} \\cdot 5\\right)^{4}}{\\left(3 \\cdot 5^{2}\\right)^{3}} = \\frac{3^{8} \\cdot 5^{4}}{3^{3} \\cdot 5^{6}} = \\frac{3^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{147^{-4}}{63^{-3}}$", "$\\displaystyle \\frac{147^{-4}}{63^{-3}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{-4}}{\\left(3^{2} \\cdot 7\\right)^{-3}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{3}}{\\left(3 \\cdot 7^{2}\\right)^{4}} = \\frac{3^{6} \\cdot 7^{3}}{3^{4} \\cdot 7^{8}} = \\frac{3^{2}}{7^{5}}$"], ["$\\displaystyle \\frac{18^{-2}}{12^{-3}}$", "$\\displaystyle \\frac{18^{-2}}{12^{-3}} = \\frac{\\left(2 \\cdot 3^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 3\\right)^{-3}} = \\frac{\\left(2^{2} \\cdot 3\\right)^{3}}{\\left(2 \\cdot 3^{2}\\right)^{2}} = \\frac{2^{6} \\cdot 3^{3}}{2^{2} \\cdot 3^{4}} = \\frac{2^{4}}{3}$"], ["$\\displaystyle \\frac{18^{-2}}{12^{-3}}$", "$\\displaystyle \\frac{18^{-2}}{12^{-3}} = \\frac{\\left(2 \\cdot 3^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 3\\right)^{-3}} = \\frac{\\left(2^{2} \\cdot 3\\right)^{3}}{\\left(2 \\cdot 3^{2}\\right)^{2}} = \\frac{2^{6} \\cdot 3^{3}}{2^{2} \\cdot 3^{4}} = \\frac{2^{4}}{3}$"], ["$\\displaystyle \\frac{45^{-3}}{75^{-2}}$", "$\\displaystyle \\frac{45^{-3}}{75^{-2}} = \\frac{\\left(3^{2} \\cdot 5\\right)^{-3}}{\\left(3 \\cdot 5^{2}\\right)^{-2}} = \\frac{\\left(3 \\cdot 5^{2}\\right)^{2}}{\\left(3^{2} \\cdot 5\\right)^{3}} = \\frac{3^{2} \\cdot 5^{4}}{3^{6} \\cdot 5^{3}} = \\frac{5}{3^{4}}$"], ["$\\displaystyle \\frac{12^{-2}}{18^{-4}}$", "$\\displaystyle \\frac{12^{-2}}{18^{-4}} = \\frac{\\left(2^{2} \\cdot 3\\right)^{-2}}{\\left(2 \\cdot 3^{2}\\right)^{-4}} = \\frac{\\left(2 \\cdot 3^{2}\\right)^{4}}{\\left(2^{2} \\cdot 3\\right)^{2}} = \\frac{2^{4} \\cdot 3^{8}}{2^{4} \\cdot 3^{2}} = 3^{6}$"]],
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ruby potenzen-und-brueche.rb 13