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konu anlatımları, yeşil sayfalarda soru avcısı sayfaları ve derece testi. İçerikte doğal sayılar, pozitif ve negatif üslü ifadeler, pozitif sayıların tüm kuvvetlerinin pozitif olması, negatif sayıların çift kuvvetlerinde eksi işaretinin kalktığı ve tek kuvvetlerinde eksi işaretinin kaldığı gibi temel prensipler örneklerle açıklanmaktadır.","Videoda ayrıca özel işlemler tanımlaması, üslü ifadelerin değerlerini hesaplama ve her zaman doğru olan ifadeleri belirleme gibi farklı soru tipleri çözülmektedir. Video, üslü sayılar konusunun birinci adımının tamamlanmasıyla sona ererken, ikinci videoda tüm ayrıntıların, tanımların, kavramların ve ispatların anlatılacağı bilgisi verilmektedir."]},"endTime":1719,"title":"9. Sınıf Matematik Dersi: Üslü Sayılar","beginTime":0}],"fullResult":[{"index":0,"title":"9. Sınıf Matematik Derslerine Giriş","list":{"type":"unordered","items":["Mehmet hocanın 2025 güncel müfredata uygun 9. sınıf matematik dersleri başlıyor.","Dersler üç aşamadan oluşacak: mavi sayfalarda konu anlatımları, yeşil sayfalarda soru avcısı sayfaları ve üçüncü aşamada derece testleri.","Dersler ücretsiz yayınlanacak, PDF'ler ise RM Akademi katıl butonuna tıklayarak erişilebilecek."]},"beginTime":0,"endTime":117,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=0&ask_summarization=1"},{"index":1,"title":"Ders Yapısı ve Temalar","list":{"type":"unordered","items":["Eskiden ünite kavramı vardı, şimdi tema kavramı kullanılıyor ve toplam yedi tema olacak.","İlk tema \"Sayılar\" olup, gerçek sayıların üstü ve köklü gösterimleri ile yapılan işlemler alt başlıklarını içeriyor.","Üslü sayılar konusuna ilk adım olarak başlanacak."]},"beginTime":117,"endTime":251,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=117&ask_summarization=1"},{"index":2,"title":"Üslü Sayıların Tanımı","list":{"type":"unordered","items":["Üslü sayı, a'dan farklı bir gerçel sayı ve n'den pozitif bir tam sayı olmak üzere a üssü n ifadesine üslü gösterim adı verilir.","a üssü n ifadesinde a taban, n ise üs olarak adlandırılır ve a sayısının n tane yan yana çarpımı anlamına gelir.","5+5+5+5+5 ifadesi 5 üzeri 5 ile karıştırılmamalı, bu ifade 5×5×5×5×5 anlamına gelir."]},"beginTime":251,"endTime":333,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=251&ask_summarization=1"},{"index":3,"title":"Üslü Sayıların Özel Durumları","list":{"type":"unordered","items":["a'dan farklı olmak üzere a üssü 0, sıfır hariç bir sayının üstüne yazıldığında o sayı daima 1 kabul edilir.","Taban sıfır olduğunda üs herhangi bir sayı olursa, bu ifade matematikte tanımlanmamış ve belirsizlik durumudur.","Herhangi bir sayı (n sıfırdan farklı) üzeri 0, her zaman 1'e eşittir."]},"beginTime":333,"endTime":416,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=333&ask_summarization=1"},{"index":4,"title":"Üslü Sayılarla İlgili Örnek Sorular","list":{"type":"unordered","items":["3 üzeri 4 ifadesi 3×3×3×3 anlamına gelir ve sonucu 81'dir.","5×5 üzeri 5 ifadesi 5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×"]},"beginTime":416,"endTime":531,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=416&ask_summarization=1"},{"index":5,"title":"Doğal Sayılar ve Üslü İfadeler","list":{"type":"unordered","items":["Doğal sayılar sıfırdan başlayıp bir, iki, üç şeklinde artı sonsuza kadar giden sayılardır.","a ve b doğal sayı olmak üzere, a üzeri b = 81 olduğunda, bu koşulu sağlayan a+b toplamının alabileceği en küçük değer 7, en büyük değer 11'dir.","81'in farklı üslü ifadeleri 9² ve 3⁴'tür, bu değerlerin toplamı 89'dur."]},"beginTime":533,"endTime":632,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=533&ask_summarization=1"},{"index":6,"title":"Negatif Üsler","list":{"type":"unordered","items":["Bir ifadenin üstüne negatif bir üs yazıldığında, amaç sayıya takla attırmaktır.","a üzeri eksi n, 1 bölü a üzeri n anlamına gelir.","Örneğin, 3 üzeri eksi 2, 1 bölü 3 üzeri 2 demektir ve sonucu 1/9'dur."]},"beginTime":632,"endTime":679,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=632&ask_summarization=1"},{"index":7,"title":"Üslü Sayılar Kuralları","list":{"type":"unordered","items":["Pozitif sayıların tüm kuvvetleri pozitiftir, örneğin 3'ün herhangi bir kuvveti pozitiftir.","Negatif sayıların çift kuvveti alındığında içerideki eksi işareti kaybolur ve sonuç pozitif olur.","Negatif sayıların tek kuvveti alındığında içerideki eksi işareti korunur ve sonuç negatif olur."]},"beginTime":681,"endTime":766,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=681&ask_summarization=1"},{"index":8,"title":"Üslü Sayılar Örnekleri","list":{"type":"unordered","items":["(-3)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç -81 olur.","(-5)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç -625 olur.","(-2)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç 16 olur."]},"beginTime":766,"endTime":872,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=766&ask_summarization=1"},{"index":9,"title":"Negatif Üslü Sayılar","list":{"type":"unordered","items":["4⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 2² = 16 olur.","(-5)⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 5² = 25 olur.","(-1/3)⁻⁴ ifadesinde üst negatif olduğu için sayı ters çevrilir ve 3⁴ = 81 olur."]},"beginTime":872,"endTime":980,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=872&ask_summarization=1"},{"index":10,"title":"Tanımsız İfadeler","list":{"type":"unordered","items":["0, 0'a bölünemez çünkü 0'ı elde etmek için çarpılacak sayı yoktur.","0, 0'a bölünemez ve bu durum matematikte tanımsızdır.","Tanımsız, bir şeyin tanımlanmamış olduğu anlamına gelir."]},"beginTime":980,"endTime":1014,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=980&ask_summarization=1"},{"index":11,"title":"Karmaşık Üslü Sayılar","list":{"type":"unordered","items":["2⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 1/2 olur.","(-3)⁻¹ ifadesinde üst negatif olduğu için sayı ters çevrilir ve -1/3 olur.","(-5)⁻¹ ifadesinde üst negatif olduğu için sayı ters çevrilir ve -1/5 olur."]},"beginTime":1014,"endTime":1141,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1014&ask_summarization=1"},{"index":12,"title":"Değişkenli Üslü Sayılar","list":{"type":"unordered","items":["a = 2 ve b = -3 olduğunda a⁻³ + b⁻² ifadesi hesaplanır.","Bir sayının üstüne üs yazıldığında parantezli yazmak zorunludur.","a⁻³ = 1/8 ve b⁻² = 1/9 olduğundan toplamları 1/8 + 1/9 = 1/72 olur."]},"beginTime":1141,"endTime":1236,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1141&ask_summarization=1"},{"index":13,"title":"Soru Avcısı Bölümü","list":{"type":"unordered","items":["Üslü sayıların birinci adım testi (soru avcısı testi) ile konu pekiştirilir.","(-2)² = 4, (-3)² = 9, (-1)² = 1 ve (-2)³ = -8 gibi temel üslü sayı değerleri kullanılır.","Üslü sayılarla ilgili basit işlemler hızlıca çözülür."]},"beginTime":1236,"endTime":1309,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1236&ask_summarization=1"},{"index":14,"title":"Üslü Sayılar Soruları","list":{"type":"unordered","items":["İlk soruda a-2b=2 eşitliği verilmiş ve (a-2)²+b² ifadesinin değeri sorulmuş, cevap 31/4 olarak bulunmuş.","İkinci soruda k⊕r=m şeklinde bir işlem tanımlanmış ve 9⊕5+3⊕2 işleminin sonucu 9 olarak hesaplanmış.","Üçüncü soruda abc tam sayı olmak üzere verilen bir simge tanımlanmış ve işlemin sonucu -17/12 olarak bulunmuş."]},"beginTime":1311,"endTime":1565,"href":"/video/preview/3183188314363314493?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1311&ask_summarization=1"},{"index":15,"title":"Özel Üslü Sayı Sorusu","list":{"type":"unordered","items":["Son soruda a bir tamsayı olmak üzere a¹=a, a⁻¹=1/a ve a⁻²=1/a² ifadelerinden hangilerinin her zaman doğrudur sorulmuş.","a⁻¹=1/a ifadesi her zaman doğrudur çünkü a⁻¹=1/a² ifadesi tanımsızdır.","Video, üslü sayılar konusunun birinci adımının sonuna gelmiş ve ikinci videoda tüm ayrıntılarıyla devam edileceği 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ise q önermesinin karşıtı q ise p, tersi p'nin değili ise q'nun değili, karşı tersi ise q ise p olur."]},"beginTime":534,"endTime":685,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=534&ask_summarization=1"},{"index":4,"title":"Karşıt ve Tersi Kavramlarının Farkı","list":{"type":"unordered","items":["Karşıt ve tersi kavramları karıştırılmamalı, karşıt karşıya geçerken tersi ise değilini alır.","Bir önerme ile karşı tersi birbirine denktir.","Örnek olarak \"x-2 ise x²=4\" önermesinin karşıtı, tersi ve karşı tersi hesaplanıyor."]},"beginTime":685,"endTime":860,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=685&ask_summarization=1"},{"index":5,"title":"İki Yönlü Koşullu Önermeler","list":{"type":"unordered","items":["p ve q önermeleri \"ancak ve ancak\" ifadesiyle birleştirildiğinde elde edilen p ancak ve ancak q önermesine iki yönlü koşullu önerme denir.","İki yönlü koşullu önermede, p ise q ve q ise p önermeleri birlikte geçerlidir.","İki yönlü koşullu önermede p ancak ve ancak q ile p'nin değili ancak ve ancak q'nun değili birbirine denktir."]},"beginTime":860,"endTime":1039,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=860&ask_summarization=1"},{"index":6,"title":"Matematik Öğrenme Tavsiyeleri","list":{"type":"unordered","items":["Koşullu önermeler konusundan korkulmamalı, ezberlenmeyip mantığa oturtulmalı ve bol soru çözülmelidir.","Matematikten korkulacak hiçbir şey yok, sadece bol soru çözülmesi gerekiyor.","Doğruluk değeri bir olan p ancak ve ancak q önermesine çift gerektirme denir."]},"beginTime":1039,"endTime":1101,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1039&ask_summarization=1"},{"index":7,"title":"Bileşik Önermeler Sorusu","list":{"type":"unordered","items":["Örnek soruda \"veya\" bağlacıyla bağlanan önermelerin çözümü gösteriliyor.","\"İse\" bağlacının kullanımı ve \"ancak ve ancak\" bağlacının işlevi açıklanıyor.","Sorunun çözümünde doğru cevabı veren öğrenciler tebrik ediliyor."]},"beginTime":1105,"endTime":1293,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1105&ask_summarization=1"},{"index":8,"title":"Açık Önermeler","list":{"type":"unordered","items":["İçinde en az bir değişken bulunan ve değişkenlere verilen değerlere göre doğru ya da yanlış olan önermelere açık önerme denir.","Açık önermelerde doğrulayan elemanların kümesine doğruluk kümesi denir.","İçinde x değişkeni bulunduran açık önermeler P(x), Q(x), R(x) biçiminde gösterilir."]},"beginTime":1293,"endTime":1370,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1293&ask_summarization=1"},{"index":9,"title":"Doğruluk Kümesi Örneği","list":{"type":"unordered","items":["P(x) önermesi: 1 ≤ x² \u003c 30 ve x ≥ 1 olan doğal sayılar şeklinde tanımlanıyor.","x yerine farklı değerler koyularak önermenin doğruluğu kontrol ediliyor.","Doğruluk kümesi: {1, 2, 3, 4, 5} olarak bulunuyor."]},"beginTime":1370,"endTime":1547,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1370&ask_summarization=1"},{"index":10,"title":"Niceleyiciler","list":{"type":"unordered","items":["Niceleyiciler, önermelerde genel bir tanım yapmak için kullanılan ifadelerdir.","Evrensel niceleyici \"her\" anlamına gelir ve ters A (∀) ile gösterilir.","Varlıksal niceleyici \"bazı\" anlamına gelir ve ters E (∃) ile gösterilir."]},"beginTime":1547,"endTime":1659,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1547&ask_summarization=1"},{"index":11,"title":"Matematiksel Önermeler ve Değil İşlemi","list":{"type":"unordered","items":["Her tam sayının karesi sıfırdan büyük olduğu iddiası yanlıştır çünkü sıfırın karesi sıfırdır.","Bazı doğal sayıların bir eksiği beşten küçük veya eşit olduğu önermesi, \"bazı x doğal sayıları için x-1 ≤ 5\" şeklinde ifade edilir.","\"Her\" kelimesinin değili \"bazı\" kelimesidir ve önermenin değili alındığında, önermenin karşıtı alınır."]},"beginTime":1667,"endTime":1902,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1667&ask_summarization=1"},{"index":12,"title":"Koşullu Önermeler ve Değil İşlemi","list":{"type":"unordered","items":["\"P ise Q\" şeklindeki koşullu önermenin değili, \"P ve Q'nin değili\" şeklinde yazılır.","Büyük eşit işareti (≥) tersi küçüktür işareti (\u003c) olur, küçük eşit işareti (≤) tersi büyüktür işareti (>) olur."]},"beginTime":1902,"endTime":2030,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=1902&ask_summarization=1"},{"index":13,"title":"Aksiyom ve Teorem Kavramları","list":{"type":"unordered","items":["Aksiyom, doğruluğu ispatsız olarak kabul edilen önermelerdir.","Teorem, doğruluğu ispatlanması gereken önermelerdir.","\"P ise Q\" şeklindeki bir teoreminde, P hipotez, Q ise hüküm olarak adlandırılır."]},"beginTime":2030,"endTime":2235,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=2030&ask_summarization=1"},{"index":14,"title":"Ödev kontrolü ve konu özeti","list":{"type":"unordered","items":["Geçen hafta pazartesi günü 12'den 21'e kadar ödev verilmiş, bugün 28 Eylül'de koşullu önermeler ve bazıları konusu işlenmiş.","Ödev kontrolü için 22,39 arası sayfalardan \"ise\" bağlacı ile başlayan konu tekrarı ve pekiştirici sorular kontrol ediliyor.","Öğrenciler \"her\" ve \"bazı\" kavramlarını mantık dilinde yazarak konuyu pekiştirmişler."]},"beginTime":2241,"endTime":2290,"href":"/video/preview/2728507297138579?parent-reqid=1769840152761842-14212855048364211853-balancer-l7leveler-kubr-yp-sas-209-BAL&text=9AXEE&t=2241&ask_summarization=1"},{"index":15,"title":"Yeni ödev ve ders sonu","list":{"type":"unordered","items":["Yeni ödev olarak kümeler konusu verilmiş, ayrıca bazı öğrenciler için Dinamo kitabından 45'e kadar mantık konusu ödevi önerilmiş.","Ders sonunda öğrencilerden like butonuna basmaları ve ödülü kazananın cevabını yoruma bırakmaları istenmiş.","Eğitmen, dersin güzel geçtiğini düşünerek 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