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This shows you the differences between two versions of the page.

--- lehrkraefte:ks:enp [2021/12/03 18:08]
Simon Knaus
+++ lehrkraefte:ks:enp [2022/01/17 17:45]
Simon Knaus
@@ Line 1: / Line 1: @@
 ===== Miniaufgaben =====
-  * Auf jede Lektion (ausser Prüfungslektionen) ist eine Miniaufgabe vorzubereiten. Am Anfang der Lektion wird eine Münze geworfen. Damit der Münzwurf gültig ist, muss sich die Münze mindestens 10 mal in der Luft drehen. Zeigt die Münze **Zahl**, wird eine Aufgabe in Form eines Kurztests geprüft.
+  * Jeweils am Freitag wird eine Miniaufgabe geprüft.
-  * Jeder Schüler hat 3 Joker für das 1. Semester. Bei Meldung per e-mail oder Threema (HX3WS583) bis spätestens 12 h vor Lektionsbeginn wird der Schüler vom eventuellen Kurztest ersatzlos dispensiert. Zeigt die Münze Kopf, ist der Joker aber auch aufgebraucht!
+  * Der Minikurztest ist auf mitgebrachtem **A4-Papier im Hochformat** zu lösen. Der Name ist **oben rechts** zu notieren.
-  * Der Minikurztest ist auf mitgebrachtem **A4-Papier im Hochformat** zu lösen. Ausgefranste Ränder, zerknittertes Papier, abgerissene Ecken und Übergrössen führen zu **Abzug**.
-  * Der Name ist **oben rechts** zu notieren.
   * Die Prüfungsblätter können mehrmals verwendet werden, die Aufgaben sind aber sauber abzugrenzen.
-  * Der Durchschnitt aller Miniaufgaben zählt als eine volle 5. Prüfungsnote.
 <PRELOAD>
@@ Line 12: / Line 9: @@
-==== 29. November 2021 bis 3. Dezember 2021 ====
+==== Miniaufgaben ====
-=== Donnerstag 2. Dezember 2021 ===
+=== KW 3===
-Resultat als Bruch von Potenzen mit positiven Exponenten von Primzahlen.<JS>miniAufgabe("#exonegex_numberpower","#solnegex_numberpower",
+Primfaktorzerlegung von Nenner und Zähler, dann kürzen und als Kehrwert verrechnen!
-[["$\\displaystyle \\frac{63^{-4}}{147^{-2}}$", "$\\displaystyle \\frac{63^{-4}}{147^{-2}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{-4}}{\\left(3 \\cdot 7^{2}\\right)^{-2}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{2}}{\\left(3^{2} \\cdot 7\\right)^{4}} = \\frac{3^{2} \\cdot 7^{4}}{3^{8} \\cdot 7^{4}} = \\frac{1}{3^{6}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-2}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-2}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-2}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{2}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{4} \\cdot 5^{2}}{2^{3} \\cdot 5^{6}} = \\frac{2}{5^{4}}$"], ["$\\displaystyle \\frac{175^{-4}}{245^{-3}}$", "$\\displaystyle \\frac{175^{-4}}{245^{-3}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{-4}}{\\left(5 \\cdot 7^{2}\\right)^{-3}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{3}}{\\left(5^{2} \\cdot 7\\right)^{4}} = \\frac{5^{3} \\cdot 7^{6}}{5^{8} \\cdot 7^{4}} = \\frac{7^{2}}{5^{5}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{147^{-2}}{63^{-4}}$", "$\\displaystyle \\frac{147^{-2}}{63^{-4}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{-2}}{\\left(3^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{4}}{\\left(3 \\cdot 7^{2}\\right)^{2}} = \\frac{3^{8} \\cdot 7^{4}}{3^{2} \\cdot 7^{4}} = 3^{6}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{8} \\cdot 5^{4}}{2^{3} \\cdot 5^{6}} = \\frac{2^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{245^{-2}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-2}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-2}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{2}} = \\frac{5^{8} \\cdot 7^{4}}{5^{2} \\cdot 7^{4}} = 5^{6}$"]],
-" <hr> ", " <hr> ");
+<JS>miniAufgabe("#exofraction1","#solfraction1",[
+	[
+		"$$\\frac{165}{195}:\\frac{231}{52}$$",
+		"$$\\frac{4}{21}$$"
+	],
+	[
+		"$$\\frac{45}{50}:\\frac{45}{385}$$",
+		"$$\\frac{77}{10}$$"
+	],
+	[
+		"$$\\frac{55}{65}:\\frac{55}{143}$$",
+		"$$\\frac{11}{5}$$"
+	],
+	[
+		"$$\\frac{49}{55}:\\frac{49}{33}$$",
+		"$$\\frac{3}{5}$$"
+	],
+	[
+		"$$\\frac{147}{165}:\\frac{175}{66}$$",
+		"$$\\frac{42}{125}$$"
+	],
+	[
+		"$$\\frac{63}{165}:\\frac{245}{847}$$",
+		"$$\\frac{33}{25}$$"
+	],
+	[
+		"$$\\frac{75}{105}:\\frac{75}{175}$$",
+		"$$\\frac{5}{3}$$"
+	],
+	[
+		"$$\\frac{175}{165}:\\frac{105}{165}$$",
+		"$$\\frac{5}{3}$$"
+	],
+	[
+		"$$\\frac{75}{75}:\\frac{27}{50}$$",
+		"$$\\frac{50}{27}$$"
+	],
+	[
+		"$$\\frac{77}{26}:\\frac{55}{26}$$",
+		"$$\\frac{7}{5}$$"
+	],
+	[
+		"$$\\frac{105}{165}:\\frac{245}{539}$$",
+		"$$\\frac{7}{5}$$"
+	],
+	[
+		"$$\\frac{15}{25}:\\frac{9}{35}$$",
+		"$$\\frac{7}{3}$$"
+	],
+	[
+		"$$\\frac{105}{30}:\\frac{45}{110}$$",
+		"$$\\frac{77}{9}$$"
+	],
+	[
+		"$$\\frac{385}{78}:\\frac{539}{195}$$",
+		"$$\\frac{25}{14}$$"
+	],
+	[
+		"$$\\frac{105}{70}:\\frac{245}{385}$$",
+		"$$\\frac{33}{14}$$"
+	],
+	[
+		"$$\\frac{245}{66}:\\frac{343}{385}$$",
+		"$$\\frac{25}{6}$$"
+	],
+	[
+		"$$\\frac{15}{35}:\\frac{25}{49}$$",
+		"$$\\frac{21}{25}$$"
+	],
+	[
+		"$$\\frac{33}{39}:\\frac{55}{143}$$",
+		"$$\\frac{11}{5}$$"
+	],
+	[
+		"$$\\frac{77}{39}:\\frac{77}{143}$$",
+		"$$\\frac{11}{3}$$"
+	]
+]," &nbsp; &nbsp; ");</JS>
+<HTML>
+<div id="exofraction1"> </div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solfraction1"></div>
+</HTML>
+</hidden>
+=== KW 2===
+Berechnen Sie:
+<JS>miniAufgabe("#exopascal1","#solpascal1",[["$$\\left(\\frac{b}{2}+2 v\\right)^4$$",   "$$\\frac{b^4}{16}+b^3 v+6 b^2 v^2+16 b v^3+16 v^4$$"], ["$$(3 a-2 b)^3$$",   "$$27 a^3-54 a^2 b+36 a b^2-8 b^3$$"], ["$$\\left(\\frac{c}{3}+3 d\\right)^5$$","$$\\frac{c^5}{243}+\\frac{5 c^4 d}{27}+\\frac{10 c^3 d^2}{3}+30c^2 d^3+135 c d^4+243 d^5$$"], ["$$(2 a-2 b)^3$$", "$$8 a^3-24 a^2 b+24 a b^2-8 b^3$$"], ["$$(c+3 d)^3$$", "$$c^3+9 c^2 d+27 c d^2+27 d^3$$"], ["$$\\left(2u-\\frac{v}{4}\\right)^3$$","$$8 u^3-3 u^2 v+\\frac{3 u v^2}{8}-\\frac{v^3}{64}$$"], ["$$\\left(\\frac{a}{2}-\\frac{b}{3}\\right)^4$$","$$\\frac{a^4}{16}-\\frac{a^3 b}{6}+\\frac{a^2 b^2}{6}-\\frac{2ab^3}{27}+\\frac{b^4}{81}$$"],["$$\\left(\\frac{x}{4}-\\frac{y}{2}\\right)^5$$", "$$\\frac{x^5}{1024}-\\frac{5 x^4 y}{512}+\\frac{5 x^3 y^2}{128}-\\frac{5 x^2 y^3}{64}+\\frac{5 x y^4}{64}-\\frac{y^5}{32}$$"]],
+" &nbsp; &nbsp; ");
 </JS>
 <HTML>
-<div id="exonegex_numberpower"></div>
+<div id="exopascal1"></div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solpascal1"></div>
+</HTML>
+</hidden>
+=== KW 1 ===
+Berechnen Sie:
+<JS>miniAufgabe("#exobruchrechnen3","#solbruchrechnen3",
+[["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]],
+" &nbsp; &nbsp; ");
+</JS>
+<HTML>
+<div id="exobruchrechnen3"></div>
 </HTML>
 <hidden Lösungen>
 <HTML>
-<div id="solnegex_numberpower"></div>
+<div id="solbruchrechnen3"></div>
-<div style='font-size:12px;color:gray;'>ruby potenzen-und-brueche.rb 13</div>
 </HTML>
+</hidden>
+=== KW 50 ===
+Berechnen Sie:
+<JS>miniAufgabe("#exobruchrechnen2","#solbruchrechnen2",
+[["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]],
+" &nbsp; &nbsp; ");
+</JS>
+<HTML>
+<div id="exobruchrechnen2"></div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solbruchrechnen2"></div>
+</HTML>
 </hidden>
-=== Freitag 3. Dezember 2021 ===
+=== KW 49 ===
-Beschreiben Sie den entsprechenden geometrischen Ort als geometrische Konstruktion:<JS>miniAufgabe("#exopractical_go","#solpractical_go",
+Resultat als Bruch von Potenzen mit positiven Exponenten von Primzahlen.<JS>miniAufgabe("#exonegex_numberpower","#solnegex_numberpower",
-[["$afg$","$123$"],["$afg$","$123$"],["$afg$","$123$"],["$afg$","$123$"]],
+[["$\\displaystyle \\frac{63^{-4}}{147^{-2}}$", "$\\displaystyle \\frac{63^{-4}}{147^{-2}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{-4}}{\\left(3 \\cdot 7^{2}\\right)^{-2}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{2}}{\\left(3^{2} \\cdot 7\\right)^{4}} = \\frac{3^{2} \\cdot 7^{4}}{3^{8} \\cdot 7^{4}} = \\frac{1}{3^{6}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-2}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-2}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-2}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{2}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{4} \\cdot 5^{2}}{2^{3} \\cdot 5^{6}} = \\frac{2}{5^{4}}$"], ["$\\displaystyle \\frac{175^{-4}}{245^{-3}}$", "$\\displaystyle \\frac{175^{-4}}{245^{-3}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{-4}}{\\left(5 \\cdot 7^{2}\\right)^{-3}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{3}}{\\left(5^{2} \\cdot 7\\right)^{4}} = \\frac{5^{3} \\cdot 7^{6}}{5^{8} \\cdot 7^{4}} = \\frac{7^{2}}{5^{5}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{147^{-2}}{63^{-4}}$", "$\\displaystyle \\frac{147^{-2}}{63^{-4}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{-2}}{\\left(3^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{4}}{\\left(3 \\cdot 7^{2}\\right)^{2}} = \\frac{3^{8} \\cdot 7^{4}}{3^{2} \\cdot 7^{4}} = 3^{6}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{8} \\cdot 5^{4}}{2^{3} \\cdot 5^{6}} = \\frac{2^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{245^{-2}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-2}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-2}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{2}} = \\frac{5^{8} \\cdot 7^{4}}{5^{2} \\cdot 7^{4}} = 5^{6}$"]],
 " <hr> ", " <hr> ");
 </JS>
 <HTML>
-<div id="exopractical_go"></div>
+<div id="exonegex_numberpower"></div>
 </HTML>
 <hidden Lösungen>
 <HTML>
-<div id="solpractical_go"></div>
+<div id="solnegex_numberpower"></div>
-<div style='font-size:12px;color:gray;'>ruby planimetrie-definitionen.rb 3</div>
+<div style='font-size:12px;color:gray;'>ruby potenzen-und-brueche.rb 13</div>
 </HTML>
 </hidden>