{"id":1420,"date":"2024-09-19T16:57:08","date_gmt":"2024-09-19T16:57:08","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1420"},"modified":"2024-09-20T03:54:00","modified_gmt":"2024-09-20T03:54:00","slug":"1-1-%cf%80%cf%81%ce%ac%ce%be%ce%b5%ce%b9%cf%82-%ce%bc%ce%b5-%cf%80%cf%81%ce%b1%ce%b3%ce%bc%ce%b1%cf%84%ce%b9%ce%ba%ce%bf%cf%8d%cf%82-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%ce%bf%cf%8d%cf%82-%ce%b4%cf%85","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1420","title":{"rendered":"\u03911.1.\u0392 \u0394\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd"},"content":{"rendered":"
\n

<\/i> \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/em><\/span><\/h4>\n<\/div>\n

\u03a0\u03c9\u03c2 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b7 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd \u03bc\u03b5 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf;<\/strong><\/span><\/em><\/p>\n

\u0397 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03bc\u03b5 \u03b2\u03ac\u03c3\u03b7 \u03ad\u03bd\u03b1\u03bd \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b1 \u03ba\u03b1\u03b9 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03ad\u03bd\u03b1\u00a0\u03c6\u03c5\u03c3\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03bd \u2265 2 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \"\gra^{\grn}\" \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf\u00a0\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03cc\u03bd\u03c4\u03c9\u03bd \u03af\u03c3\u03c9\u03bd \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b1. \u0394\u03b7\u03bb\u03b1\u03b4\u03ae,<\/p>\n

\"\"<\/p>\n

\u039f\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b1\u03ba\u03cc\u03bc\u03b7:<\/p>\n

    \n
  • \u00a0\"\gra^1=\gra\"<\/li>\n
  • \"\gra^0=1 \quad\" \u03bc\u03b5 \"\gra\neq 0\"<\/li>\n
  • \"\gra^{-\grn}=\dfrac{1}{\gra^{\grn}} \quad\" \u03bc\u03b5 \"\gra\neq 0\"<\/li>\n<\/ul>\n

    \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03c9\u03bd \u03bc\u03b5 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf;<\/span><\/strong><\/em><\/p>\n

    \u039f\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03c9\u03bd \u03bc\u03b5 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf, \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03c1\u03bf\u03cb\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03c6\u03bf\u03c1\u03ac \u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03b9 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2<\/strong> \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03c0\u03bf\u03c5 \u03c3\u03b7\u03bc\u03b5\u03b9\u03ce\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9<\/strong>, \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b5\u03be\u03ae\u03c2:<\/p>\n

      \n
    • \"\gra^{\grk}\cdot\gra^{\grl}=\gra^{\grk+\grl}\"<\/li>\n
    • \"\dfrac{\gra^{\grk}}{\gra^{\grl}}=\gra^{\grk-\grl}\"<\/li>\n
    • \u00a0\"(\gra\cdot\grb)^{\grk}=\gra^{\grk}\cdot\gra^{\grl}\"<\/li>\n
    • \u00a0\"\left(\dfrac{\gra}{\grb}\right)^{\grk}=\dfrac{\gra^{\grk}}{\gra^{\grk}}\"<\/li>\n
    • \u00a0\"\left(\gra^{\grk}\right)^{\grl}=\gra^{\grk\cdot\grl}\"<\/li>\n
    • \"\left(\dfrac{\gra}{\grb}\right)^{-\grn}=\left(\dfrac{\grb}{\gra}\right)^{\grn}\"<\/li>\n<\/ul>\n

      <\/i> \u00a0\u03a0\u03b1\u03c1\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b7: \u00a0<\/span><\/i><\/b>H \u03c0\u03c1\u03bf\u03c4\u03b5\u03c1\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03c0\u03c1\u03ac\u03be\u03b5\u03c9\u03bd \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2:<\/p>\n

        \n
      • \u00a0\u03a0\u03c1\u03ce\u03c4\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2.<\/li>\n
      • \u03a3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03b1\u03c3\u03bc\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c3\u03b5\u03b9\u03c2.<\/li>\n
      • \u03a4\u03ad\u03bb\u03bf\u03c2, \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03c1\u03bf\u03c3\u03b8\u03ad\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b1\u03c6\u03b1\u03b9\u03c1\u03ad\u03c3\u03b5\u03b9\u03c2.<\/li>\n<\/ul>\n

        \u038c\u03c4\u03b1\u03bd \u03b7 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b5\u03bd\u03b8\u03ad\u03c3\u03b5\u03b9\u03c2, \u03b5\u03ba\u03c4\u03b5\u03bb\u03bf\u03cd\u03bc\u03b5 \u03c0\u03c1\u03ce\u03c4\u03b1 \u03c4\u03b9\u03c2 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03bc\u03ad\u03c3\u03b1 \u03c3\u03c4\u03b9\u03c2 \u03c0\u03b1\u03c1\u03b5\u03bd\u03b8\u03ad\u03c3\u03b5\u03b9\u03c2 \u03bc\u03b5 \u03c4\u03b7 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b1\u03bc\u03b5 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9.<\/p>\n

         <\/p>\n

        <\/i> Let’s Practise<\/strong><\/span><\/em><\/h4>\n

        1. \u039d\u03b1 \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2:<\/em><\/span><\/strong><\/p>\n

        \n
        \u03b1.<\/strong> \"\dfrac{(x^3 \cdot x^{-2})^4}{x^5 \cdot x^{-1}}\"<\/p>\n

        \u03b2.<\/strong> \"(y^2 \cdot y^3)^{3} \cdot y^{-5}\"<\/p>\n

        \u03b3.<\/strong> \"\dfrac{(\alpha^4)^3 \cdot \alpha^{-2}}{(\alpha^2)^4}\"<\/p>\n

        \u03b4.<\/strong> \"\dfrac{(\beta^5 \cdot \beta^{-2})^2}{(\beta^3 \cdot \beta^{-1})^3}\"<\/p>\n

        \u03b5.<\/strong> \"\dfrac{x^{6} \cdot (x^{-2})^3}{x^5}\"<\/div>\n

        \u03c3\u03c4.<\/strong> \"(\alpha^3 \cdot \alpha^4)^{-2} \cdot \alpha^5\"<\/p>\n

        \u03b6.<\/strong> \"\dfrac{(y^2)^4 \cdot y^{-3}}{(y^{-2})^2}\"<\/p>\n

        \u03b7.<\/strong> \"(x^{-3} \cdot x^2)^4 \cdot x^{-6}\"<\/p>\n

        \u03b8.<\/strong> \"\dfrac{(\beta^{-5})^2}{\beta^{-4} \cdot \beta^3}\"<\/p>\n

        \u03b9.<\/strong> \"\dfrac{(\alpha^4 \cdot \alpha^{-2})^3}{\alpha^5 \cdot \alpha^{-7}}\"<\/div>\n<\/div>\n

         <\/p>\n

        2. \u039d\u03b1 \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2:<\/span><\/em><\/strong><\/p>\n

        \n
        \n

        \u03b1.<\/strong> \"\dfrac{(x^2 \cdot y^3)^2}{x^3 \cdot y^5}\"<\/p>\n

        \u03b2.<\/strong> \"(x^3 \cdot y^{-2})^4 \cdot x^{-6}\"<\/p>\n

        \u03b3.<\/strong> \"\dfrac{(x^5 \cdot y^4)^3}{x^4 \cdot (y^{-3})^2}\"<\/p>\n

        \u03b4.<\/strong> \"\dfrac{(\alpha^3 \cdot \beta^{-1})^2}{\alpha^4 \cdot \beta^{-3}}\"<\/p>\n

        \u03b5.<\/strong> \"(x^2 \cdot y^{-1})^3 \cdot \dfrac{x^5}{y^4}\"<\/p>\n<\/div>\n

        \n

        \u03c3\u03c4.<\/strong> \"\dfrac{(\alpha^4 \cdot \beta^2)^5}{\alpha^3 \cdot \beta^6}\"<\/p>\n

        \u03b6.<\/strong> \"(x^{-3} \cdot y^5) \cdot \dfrac{(x^2)^3}{y^{-4}}\"<\/p>\n

        \u03b7.<\/strong> \"\dfrac{(\alpha^6 \cdot \beta^3)^2}{\alpha^{-5} \cdot \beta^2}\"<\/p>\n

        \u03b8.<\/strong> \"(x^4 \cdot y^2)^{-3} \cdot (x^{-2} \cdot y)^2\"<\/p>\n

        \u03b9.<\/strong> \"\dfrac{(\alpha^5 \cdot \beta^{-2})^4}{(\alpha^3 \cdot \beta^5)^2}\"<\/p>\n<\/div>\n<\/div>\n

        \n

        \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong> \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u0393 \u0393\u03c5\u03bc\u03bd\u03b1\u03c3\u03af\u03bf\u03c5 (\u0394\u03b7\u03bc\u03ae\u03c4\u03c1\u03b9\u03bf\u03c2 \u0391\u03c1\u03b3\u03c5\u03c1\u03ac\u03ba\u03b7\u03c2 , \u03a0\u03b1\u03bd\u03b1\u03b3\u03b9\u03ce\u03c4\u03b7\u03c2 \u0392\u03bf\u03c5\u03c1\u03b3\u03ac\u03bd\u03b1\u03c2, \u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2 \u039c\u03b5\u03bd\u03c4\u03ae\u03c2, \u03a3\u03c4\u03b1\u03bc\u03b1\u03c4\u03bf\u03cd\u03bb\u03b1 \u03a4\u03c3\u03b9\u03ba\u03bf\u03c0\u03bf\u03cd\u03bb\u03bf\u03c5, \u039c\u03b9\u03c7\u03b1\u03ae\u03bb \u03a7\u03c1\u03c5\u03c3\u03bf\u03b2\u03ad\u03c1\u03b3\u03b7\u03c2 \u03a5.\u03a0\u0391\u0399.\u0398.)<\/p>\n

        Creative Commons \u0391\u03bd\u03b1\u03c6\u03bf\u03c1\u03ac \u0394\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03bf\u03cd – \u039c\u03b7 \u0395\u03bc\u03c0\u03bf\u03c1\u03b9\u03ba\u03ae \u03a7\u03c1\u03ae\u03c3\u03b7 – \u03a0\u03b1\u03c1\u03cc\u03bc\u03bf\u03b9\u03b1 \u0394\u03b9\u03b1\u03bd\u03bf\u03bc\u03ae 4.0 \u0394\u03b9\u03b5\u03b8\u03bd\u03ad\u03c2<\/strong><\/p>\n

        \"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03a0\u03c9\u03c2 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b7 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd \u03bc\u03b5 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf; \u0397 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03bc\u03b5 \u03b2\u03ac\u03c3\u03b7 \u03ad\u03bd\u03b1\u03bd \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b1 \u03ba\u03b1\u03b9 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03ad\u03bd\u03b1\u00a0\u03c6\u03c5\u03c3\u03b9\u03ba\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03bd \u2265 2 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf\u00a0\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03cc\u03bd\u03c4\u03c9\u03bd \u03af\u03c3\u03c9\u03bd \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b1. \u0394\u03b7\u03bb\u03b1\u03b4\u03ae, \u039f\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b1\u03ba\u03cc\u03bc\u03b7: \u00a0 \u03bc\u03b5 \u03bc\u03b5 \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03b4\u03c5\u03bd\u03ac\u03bc\u03b5\u03c9\u03bd…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[40],"tags":[],"class_list":["post-1420","post","type-post","status-publish","format-standard","hentry","category-1--"],"featured_image_src":null,"author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n\u03911.1.\u0392 \u0394\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd - 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