miniaufgabe.js
==== 13. Februar 2023 bis 17. Februar 2023 ====
=== Montag 13. Februar 2023 ===
Schreiben Sie als eine einzige Potenz der Variable.miniAufgabe("#exorationalexponents2","#solrationalexponents2",
[["$\\displaystyle \\left(n^{-\\frac{5}{9}} \\cdot n^{-\\frac{1}{4}}\\right)^{-\\frac{54}{29}}$", "$\\displaystyle \\left(n^{-\\frac{5}{9}} \\cdot n^{-\\frac{1}{4}}\\right)^{-\\frac{54}{29}} = \\left(n^{-\\frac{29}{36}}\\right)^{-\\frac{54}{29}} = n^{\\frac{3}{2}}$"], ["$\\displaystyle \\left(a^{-\\frac{1}{2}} \\cdot a^{-\\frac{2}{3}}\\right)^{\\frac{27}{14}}$", "$\\displaystyle \\left(a^{-\\frac{1}{2}} \\cdot a^{-\\frac{2}{3}}\\right)^{\\frac{27}{14}} = \\left(a^{-\\frac{7}{6}}\\right)^{\\frac{27}{14}} = a^{-\\frac{9}{4}}$"], ["$\\displaystyle \\left(f^{\\frac{3}{7}} \\cdot f^{-\\frac{3}{2}}\\right)^{\\frac{28}{45}}$", "$\\displaystyle \\left(f^{\\frac{3}{7}} \\cdot f^{-\\frac{3}{2}}\\right)^{\\frac{28}{45}} = \\left(f^{-\\frac{15}{14}}\\right)^{\\frac{28}{45}} = f^{-\\frac{2}{3}}$"], ["$\\displaystyle \\left(k^{\\frac{5}{8}} \\cdot k^{-\\frac{2}{9}}\\right)^{\\frac{60}{29}}$", "$\\displaystyle \\left(k^{\\frac{5}{8}} \\cdot k^{-\\frac{2}{9}}\\right)^{\\frac{60}{29}} = \\left(k^{\\frac{29}{72}}\\right)^{\\frac{60}{29}} = k^{\\frac{5}{6}}$"], ["$\\displaystyle \\left(a^{-\\frac{5}{3}} \\cdot a^{-\\frac{2}{5}}\\right)^{-\\frac{35}{93}}$", "$\\displaystyle \\left(a^{-\\frac{5}{3}} \\cdot a^{-\\frac{2}{5}}\\right)^{-\\frac{35}{93}} = \\left(a^{-\\frac{31}{15}}\\right)^{-\\frac{35}{93}} = a^{\\frac{7}{9}}$"], ["$\\displaystyle \\left(f^{-\\frac{3}{2}} \\cdot f^{-\\frac{2}{7}}\\right)^{-\\frac{56}{75}}$", "$\\displaystyle \\left(f^{-\\frac{3}{2}} \\cdot f^{-\\frac{2}{7}}\\right)^{-\\frac{56}{75}} = \\left(f^{-\\frac{25}{14}}\\right)^{-\\frac{56}{75}} = f^{\\frac{4}{3}}$"], ["$\\displaystyle \\left(y^{-\\frac{8}{3}} \\cdot y^{-\\frac{3}{2}}\\right)^{-\\frac{4}{75}}$", "$\\displaystyle \\left(y^{-\\frac{8}{3}} \\cdot y^{-\\frac{3}{2}}\\right)^{-\\frac{4}{75}} = \\left(y^{-\\frac{25}{6}}\\right)^{-\\frac{4}{75}} = y^{\\frac{2}{9}}$"], ["$\\displaystyle \\left(k^{\\frac{9}{4}} \\cdot k^{-\\frac{7}{8}}\\right)^{-\\frac{16}{33}}$", "$\\displaystyle \\left(k^{\\frac{9}{4}} \\cdot k^{-\\frac{7}{8}}\\right)^{-\\frac{16}{33}} = \\left(k^{\\frac{11}{8}}\\right)^{-\\frac{16}{33}} = k^{-\\frac{2}{3}}$"], ["$\\displaystyle \\left(m^{\\frac{2}{7}} \\cdot m^{\\frac{2}{9}}\\right)^{-\\frac{63}{64}}$", "$\\displaystyle \\left(m^{\\frac{2}{7}} \\cdot m^{\\frac{2}{9}}\\right)^{-\\frac{63}{64}} = \\left(m^{\\frac{32}{63}}\\right)^{-\\frac{63}{64}} = m^{-\\frac{1}{2}}$"], ["$\\displaystyle \\left(p^{\\frac{3}{2}} \\cdot p^{-\\frac{2}{3}}\\right)^{\\frac{21}{5}}$", "$\\displaystyle \\left(p^{\\frac{3}{2}} \\cdot p^{-\\frac{2}{3}}\\right)^{\\frac{21}{5}} = \\left(p^{\\frac{5}{6}}\\right)^{\\frac{21}{5}} = p^{\\frac{7}{2}}$"]],
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ruby kopfrechnen-rationale-exponenten.rb 2
=== Dienstag 14. Februar 2023 ===
**Robotik im E24 um 9:28**, Mathe um 13:55 im E21
Vereinfachen Sie und Schreiben Sie das Resultat als Bruch von Potenzen mit positiven Exponenten.miniAufgabe("#exorationalexponents3","#solrationalexponents3",
[["$\\displaystyle \\frac{\\left(n^{\\frac{6}{7}} \\cdot y^{\\frac{67}{63}}\\right)^{-\\frac{7}{5}}}{\\left(n^{-\\frac{93}{70}} \\cdot y^{-\\frac{2}{3}}\\right)^{\\frac{4}{3}}}$", "$\\displaystyle \\frac{\\left(n^{\\frac{6}{7}} \\cdot y^{\\frac{67}{63}}\\right)^{-\\frac{7}{5}}}{\\left(n^{-\\frac{93}{70}} \\cdot y^{-\\frac{2}{3}}\\right)^{\\frac{4}{3}}} = \\frac{n^{-\\frac{6}{5}} \\cdot y^{-\\frac{67}{45}}}{n^{-\\frac{62}{35}} \\cdot y^{-\\frac{8}{9}}} = \\frac{n^{-\\frac{42}{35}} \\cdot y^{-\\frac{67}{45}}}{n^{-\\frac{62}{35}} \\cdot y^{-\\frac{40}{45}}} = \\frac{n^{\\frac{20}{35}}}{y^{\\frac{27}{45}}} = \\frac{n^{\\frac{4}{7}}}{y^{\\frac{3}{5}}} $"], ["$\\displaystyle \\frac{\\left(e^{\\frac{55}{32}} \\cdot x^{\\frac{49}{24}}\\right)^{-\\frac{8}{7}}}{\\left(e^{\\frac{10}{21}} \\cdot x^{\\frac{23}{9}}\\right)^{-\\frac{3}{2}}}$", "$\\displaystyle \\frac{\\left(e^{\\frac{55}{32}} \\cdot x^{\\frac{49}{24}}\\right)^{-\\frac{8}{7}}}{\\left(e^{\\frac{10}{21}} \\cdot x^{\\frac{23}{9}}\\right)^{-\\frac{3}{2}}} = \\frac{e^{-\\frac{55}{28}} \\cdot x^{-\\frac{7}{3}}}{e^{-\\frac{5}{7}} \\cdot x^{-\\frac{23}{6}}} = \\frac{e^{-\\frac{55}{28}} \\cdot x^{-\\frac{14}{6}}}{e^{-\\frac{20}{28}} \\cdot x^{-\\frac{23}{6}}} = \\frac{x^{\\frac{9}{6}}}{e^{\\frac{35}{28}}} = \\frac{x^{\\frac{3}{2}}}{e^{\\frac{5}{4}}} $"], ["$\\displaystyle \\frac{\\left(x^{\\frac{14}{3}} \\cdot w^{\\frac{7}{2}}\\right)^{\\frac{1}{2}}}{\\left(x^{-\\frac{7}{3}} \\cdot w^{-\\frac{45}{8}}\\right)^{-\\frac{2}{5}}}$", "$\\displaystyle \\frac{\\left(x^{\\frac{14}{3}} \\cdot w^{\\frac{7}{2}}\\right)^{\\frac{1}{2}}}{\\left(x^{-\\frac{7}{3}} \\cdot w^{-\\frac{45}{8}}\\right)^{-\\frac{2}{5}}} = \\frac{x^{\\frac{7}{3}} \\cdot w^{\\frac{7}{4}}}{x^{\\frac{14}{15}} \\cdot w^{\\frac{9}{4}}} = \\frac{x^{\\frac{35}{15}} \\cdot w^{\\frac{7}{4}}}{x^{\\frac{14}{15}} \\cdot w^{\\frac{9}{4}}} = \\frac{x^{\\frac{21}{15}}}{w^{\\frac{2}{4}}} = \\frac{x^{\\frac{7}{5}}}{w^{\\frac{1}{2}}} $"], ["$\\displaystyle \\frac{\\left(b^{\\frac{4}{27}} \\cdot h^{-\\frac{41}{36}}\\right)^{\\frac{3}{2}}}{\\left(b^{-\\frac{29}{84}} \\cdot h^{-\\frac{5}{16}}\\right)^{\\frac{8}{3}}}$", "$\\displaystyle \\frac{\\left(b^{\\frac{4}{27}} \\cdot h^{-\\frac{41}{36}}\\right)^{\\frac{3}{2}}}{\\left(b^{-\\frac{29}{84}} \\cdot h^{-\\frac{5}{16}}\\right)^{\\frac{8}{3}}} = \\frac{b^{\\frac{2}{9}} \\cdot h^{-\\frac{41}{24}}}{b^{-\\frac{58}{63}} \\cdot h^{-\\frac{5}{6}}} = \\frac{b^{\\frac{14}{63}} \\cdot h^{-\\frac{41}{24}}}{b^{-\\frac{58}{63}} \\cdot h^{-\\frac{20}{24}}} = \\frac{b^{\\frac{72}{63}}}{h^{\\frac{21}{24}}} = \\frac{b^{\\frac{8}{7}}}{h^{\\frac{7}{8}}} $"], ["$\\displaystyle \\frac{\\left(k^{\\frac{7}{9}} \\cdot e^{-\\frac{77}{54}}\\right)^{\\frac{3}{2}}}{\\left(k^{\\frac{3}{8}} \\cdot e^{\\frac{45}{16}}\\right)^{-\\frac{4}{9}}}$", "$\\displaystyle \\frac{\\left(k^{\\frac{7}{9}} \\cdot e^{-\\frac{77}{54}}\\right)^{\\frac{3}{2}}}{\\left(k^{\\frac{3}{8}} \\cdot e^{\\frac{45}{16}}\\right)^{-\\frac{4}{9}}} = \\frac{k^{\\frac{7}{6}} \\cdot e^{-\\frac{77}{36}}}{k^{-\\frac{1}{6}} \\cdot e^{-\\frac{5}{4}}} = \\frac{k^{\\frac{7}{6}} \\cdot e^{-\\frac{77}{36}}}{k^{-\\frac{1}{6}} \\cdot e^{-\\frac{45}{36}}} = \\frac{k^{\\frac{8}{6}}}{e^{\\frac{32}{36}}} = \\frac{k^{\\frac{4}{3}}}{e^{\\frac{8}{9}}} $"], ["$\\displaystyle \\frac{\\left(e^{-\\frac{17}{2}} \\cdot a^{\\frac{7}{3}}\\right)^{\\frac{1}{3}}}{\\left(e^{-\\frac{20}{9}} \\cdot a^{\\frac{25}{54}}\\right)^{\\frac{3}{5}}}$", "$\\displaystyle \\frac{\\left(e^{-\\frac{17}{2}} \\cdot a^{\\frac{7}{3}}\\right)^{\\frac{1}{3}}}{\\left(e^{-\\frac{20}{9}} \\cdot a^{\\frac{25}{54}}\\right)^{\\frac{3}{5}}} = \\frac{e^{-\\frac{17}{6}} \\cdot a^{\\frac{7}{9}}}{e^{-\\frac{4}{3}} \\cdot a^{\\frac{5}{18}}} = \\frac{e^{-\\frac{17}{6}} \\cdot a^{\\frac{14}{18}}}{e^{-\\frac{8}{6}} \\cdot a^{\\frac{5}{18}}} = \\frac{a^{\\frac{9}{18}}}{e^{\\frac{9}{6}}} = \\frac{a^{\\frac{1}{2}}}{e^{\\frac{3}{2}}} $"], ["$\\displaystyle \\frac{\\left(n^{\\frac{63}{64}} \\cdot f^{\\frac{11}{36}}\\right)^{-\\frac{8}{7}}}{\\left(n^{-\\frac{19}{9}} \\cdot f^{\\frac{8}{21}}\\right)^{\\frac{9}{8}}}$", "$\\displaystyle \\frac{\\left(n^{\\frac{63}{64}} \\cdot f^{\\frac{11}{36}}\\right)^{-\\frac{8}{7}}}{\\left(n^{-\\frac{19}{9}} \\cdot f^{\\frac{8}{21}}\\right)^{\\frac{9}{8}}} = \\frac{n^{-\\frac{9}{8}} \\cdot f^{-\\frac{22}{63}}}{n^{-\\frac{19}{8}} \\cdot f^{\\frac{3}{7}}} = \\frac{n^{-\\frac{9}{8}} \\cdot f^{-\\frac{22}{63}}}{n^{-\\frac{19}{8}} \\cdot f^{\\frac{27}{63}}} = \\frac{n^{\\frac{10}{8}}}{f^{\\frac{49}{63}}} = \\frac{n^{\\frac{5}{4}}}{f^{\\frac{7}{9}}} $"], ["$\\displaystyle \\frac{\\left(x^{\\frac{4}{9}} \\cdot n^{\\frac{31}{27}}\\right)^{-\\frac{3}{2}}}{\\left(x^{\\frac{25}{9}} \\cdot n^{\\frac{25}{18}}\\right)^{-\\frac{2}{5}}}$", "$\\displaystyle \\frac{\\left(x^{\\frac{4}{9}} \\cdot n^{\\frac{31}{27}}\\right)^{-\\frac{3}{2}}}{\\left(x^{\\frac{25}{9}} \\cdot n^{\\frac{25}{18}}\\right)^{-\\frac{2}{5}}} = \\frac{x^{-\\frac{2}{3}} \\cdot n^{-\\frac{31}{18}}}{x^{-\\frac{10}{9}} \\cdot n^{-\\frac{5}{9}}} = \\frac{x^{-\\frac{6}{9}} \\cdot n^{-\\frac{31}{18}}}{x^{-\\frac{10}{9}} \\cdot n^{-\\frac{10}{18}}} = \\frac{x^{\\frac{4}{9}}}{n^{\\frac{21}{18}}} = \\frac{x^{\\frac{4}{9}}}{n^{\\frac{7}{6}}} $"], ["$\\displaystyle \\frac{\\left(x^{\\frac{3}{2}} \\cdot h^{-\\frac{7}{9}}\\right)^{-\\frac{9}{5}}}{\\left(x^{\\frac{27}{10}} \\cdot h^{-\\frac{23}{25}}\\right)^{-\\frac{5}{9}}}$", "$\\displaystyle \\frac{\\left(x^{\\frac{3}{2}} \\cdot h^{-\\frac{7}{9}}\\right)^{-\\frac{9}{5}}}{\\left(x^{\\frac{27}{10}} \\cdot h^{-\\frac{23}{25}}\\right)^{-\\frac{5}{9}}} = \\frac{x^{-\\frac{27}{10}} \\cdot h^{\\frac{7}{5}}}{x^{-\\frac{3}{2}} \\cdot h^{\\frac{23}{45}}} = \\frac{x^{-\\frac{27}{10}} \\cdot h^{\\frac{63}{45}}}{x^{-\\frac{15}{10}} \\cdot h^{\\frac{23}{45}}} = \\frac{h^{\\frac{40}{45}}}{x^{\\frac{12}{10}}} = \\frac{h^{\\frac{8}{9}}}{x^{\\frac{6}{5}}} $"], ["$\\displaystyle \\frac{\\left(h^{\\frac{13}{35}} \\cdot c^{\\frac{3}{14}}\\right)^{-\\frac{7}{3}}}{\\left(h^{\\frac{4}{9}} \\cdot c^{-\\frac{50}{27}}\\right)^{\\frac{3}{4}}}$", "$\\displaystyle \\frac{\\left(h^{\\frac{13}{35}} \\cdot c^{\\frac{3}{14}}\\right)^{-\\frac{7}{3}}}{\\left(h^{\\frac{4}{9}} \\cdot c^{-\\frac{50}{27}}\\right)^{\\frac{3}{4}}} = \\frac{h^{-\\frac{13}{15}} \\cdot c^{-\\frac{1}{2}}}{h^{\\frac{1}{3}} \\cdot c^{-\\frac{25}{18}}} = \\frac{h^{-\\frac{13}{15}} \\cdot c^{-\\frac{9}{18}}}{h^{\\frac{5}{15}} \\cdot c^{-\\frac{25}{18}}} = \\frac{c^{\\frac{16}{18}}}{h^{\\frac{18}{15}}} = \\frac{c^{\\frac{8}{9}}}{h^{\\frac{6}{5}}} $"]],
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ruby kopfrechnen-rationale-exponenten.rb 3