{"id":1056,"date":"2022-03-07T14:02:18","date_gmt":"2022-03-07T14:02:18","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/druhy-exponentu\/"},"modified":"2022-03-23T09:21:08","modified_gmt":"2022-03-23T09:21:08","slug":"druhy-exponentu","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/druhy-exponentu\/","title":{"rendered":"Druhy exponent\u016f"},"content":{"rendered":"

Umoc\u0148ov\u00e1n\u00ed je matematick\u00e1 operace, kter\u00e1 vyjad\u0159uje opakovan\u00e9 n\u00e1soben\u00ed<\/strong>.<\/p>\n

Umoc\u0144ov\u00e1n\u00ed m\u00e1 n\u00e1sleduj\u00edc\u00ed tvar:<\/p>\n

$${a}^{n}$$<\/p>\n

a<\/strong><\/em> je z\u00e1klad mocniny<\/strong> neboli mocn\u011bnec, n<\/strong><\/em> je mocnitel neboli exponent<\/strong>.<\/p>\n

$${2}^{3}$$<\/p>\n

V tomto p\u0159\u00edpad\u011b je 2<\/strong> z\u00e1kladem mocniny a 3<\/strong> je exponentem.<\/p>\n

P\u0159irozen\u00fd exponent<\/h2>\n
    \n
  • Pr\u00e1ce s p\u0159irozen\u00fdm exponentem je snadn\u00e1.<\/li>\n
  • Exponent n\u00e1m ur\u010duje, kolikr\u00e1t mocn\u011bnec vyn\u00e1sob\u00edme sebou sam\u00fdm<\/strong>.<\/li>\n<\/ul>\n

    $${5}^{3}= 5\\cdot5\\cdot5=125$$<\/p>\n

    $${x}^{3}= x\\cdot x\\cdot x$$<\/p>\n

    $${(-5)}^{3}= (-5)\\cdot(-5)\\cdot(-5)=-125$$<\/p>\n

    $${5}^{0}= 1$$<\/p>\n

    Z\u00e1porn\u00fd exponent<\/h2>\n
      \n
    • Jestli\u017ee je exponent z\u00e1porn\u00fd, znamen\u00e1 to jedin\u00e9: budeme d\u011blit<\/li>\n<\/ul>\n

      $${a}^{-1}=\\frac{1}{a}$$<\/p>\n

      $${3}^{-1}=\\frac{1}{3}$$<\/p>\n

      $${3}^{-1}=\\frac{1}{3}$$<\/p>\n

      $${3}^{-2}=\\frac{1}{{3}^{2}}=\\frac{1}{9}$$<\/p>\n

      $${(x+1)}^{-2}=\\frac{1}{{(x+1)}^{2}}$$<\/p>\n

      Racion\u00e1ln\u00ed exponent<\/h2>\n
        \n
      • Jakmile um\u00edme pracovat s p\u0159irozen\u00fdm i z\u00e1porn\u00fdm exponentem, m\u016f\u017eeme se vrhnout na racion\u00e1ln\u00ed exponent<\/li>\n<\/ul>\n

        $${a}^{\\frac{m}{n}}=\\sqrt[n]{{a}^{m}}$$<\/p>\n

        $${6}^{\\frac{4}{3}}=\\sqrt[3]{{6}^{4}}$$<\/p>\n

        $${3}^{\\frac{5}{3}}=\\sqrt[3]{{3}^{5}}$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1056","lesson","type-lesson","status-publish","hentry"],"yoast_head":"\nDruhy exponent\u016f | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/druhy-exponentu\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Druhy exponent\u016f | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Umoc\u0148ov\u00e1n\u00ed je matematick\u00e1 operace, kter\u00e1 vyjad\u0159uje opakovan\u00e9 n\u00e1soben\u00ed. Umoc\u0144ov\u00e1n\u00ed m\u00e1 n\u00e1sleduj\u00edc\u00ed tvar: $${a}^{n}$$ a je z\u00e1klad mocniny neboli mocn\u011bnec, n je mocnitel neboli exponent. $${2}^{3}$$ V tomto p\u0159\u00edpad\u011b je 2 z\u00e1kladem mocniny a 3 je exponentem. P\u0159irozen\u00fd exponent Pr\u00e1ce s p\u0159irozen\u00fdm exponentem je snadn\u00e1. Exponent n\u00e1m ur\u010duje, kolikr\u00e1t mocn\u011bnec vyn\u00e1sob\u00edme sebou sam\u00fdm. $${5}^{3}= 5cdot5cdot5=125$$ $${x}^{3}= ... 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