{"id":317866,"date":"2024-02-26T12:27:27","date_gmt":"2024-02-26T05:27:27","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=317866"},"modified":"2024-02-26T12:27:29","modified_gmt":"2024-02-26T05:27:29","slug":"sifat-eksponen-pengertian-sifat-penerapan-dan-contoh-soal","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/sifat-eksponen-pengertian-sifat-penerapan-dan-contoh-soal\/","title":{"rendered":"Sifat Eksponen &#8211; Pengertian, Sifat, Penerapan, dan Contoh Soal"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/Image-Newsletter-1.png\" alt=\"\" class=\"wp-image-317867\" style=\"object-fit:cover\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/Image-Newsletter-1.png 960w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/Image-Newsletter-1-768x432.png 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat dan tetap semangat, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apakah Quipperian sudah pernah belajar tentang bilangan eksponen? Tahukah kamu jika keberadaan eksponen sangat bermanfaat lho dalam kehidupan sehari-hari. Misalnya saja saat kamu diminta untuk menyebutkan kecepatan cahaya, massa Bumi, jarak antara Bumi dan bulan, dan masih banyak lainnya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sementara iyu, operasi bilangan eksponen memenuhi sifat-sifat tertentu yang biasa disebut sebagai sifat eksponen. Ingin tahu selengkapnya? Yuk, check this out!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Pengertian Eksponen<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Eksponen atau biasa disebut bilangan berpangkat adalah bentuk perkalian bilangan dengan bilangan yang sama secara berulang-ulang. Misalnya perkalian bilangan 2 dengan dirinya sendiri sebanyak tiga kali, yaitu 2 \u00d7 2 \u00d7 2. Jika dinyatakan dalam bentuk eksponen, perkalian itu bisa ditulis menjadi 2<sup>3<\/sup>. Pangkat tiga menunjukkan banyaknya pengulangan angka yang dikali. Adapun bentuk umum eksponen adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><i>a<sup>n<\/sup><\/i> dengan syarat <i>a<\/i> \u2260 1 dan <i>n<\/i> \u2208 R<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keterangan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>a<\/em> biasa disebut sebagai bilangan pokok atau basis; dan<br><em>n<\/em> disebut sebagai eskponen atau pangkat.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari bentuk umum di atas diperoleh kesimpulan bahwa bilangan yang dipangkatkan (basis) tidak boleh bernilai satu dan pangkatnya masih termasuk anggota himpunan bilangan real. Mengapa basis tidak boleh satu? Karena berapapun pangkatnya jika basisnya satu maka hasilnya akan selalu satu.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Sifat-Sifat Eksponen<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah Quipperian tahu apa itu eksponen, kini saatnya belajar sifat-sifat apa saja sih yang berlaku pada operasi eksponen?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Operasi Penjumlahan Pangkat<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat pertama ini berlaku untuk penjumlahan pangkat pada dua atau lebih bilangan eksponen, bukan penjumlahan antarbilangannya ya. Jika dua atau lebih bilangan eksponen kamu kalikan, maka kamu bisa menjumlahkan pangkatnya dengan syarat basis bilangannya harus sama. Jika basisnya tidak sama, kamu tidak bisa menjumlahkan pangkatnya. Perhatikan bentuk di bawah ini:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"1600\" height=\"361\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12.png\" alt=\"\" class=\"wp-image-317872\" style=\"width:120px\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12.png 1600w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12-768x173.png 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12-1536x347.png 1536w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12-1200x271.png 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-12-1170x264.png 1170w\" sizes=\"(max-width: 1600px) 100vw, 1600px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Contohnya, 5<sup>3<\/sup> \u00d7 5<sup>4<\/sup> = 5<sup>3+4<\/sup> = 5<sup>7<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk memudahkanmu ingat pernyataan \u201cmengalikan bilangan berpangkat dengan bilangan pokok dasar yang sama, sama artinya dengan menjumlahkan pangkatnya\u201d.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Operasi Pengurangan Pangkat<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Pada prinsipnya, sifat operasi pengurangan pangkat sama seperti penjumlahan pangkat. Jika penjumlahan pangkat berlaku untuk perkalian dua atau lebih eksponen, maka pada pengurangan berlaku pembagian dua atau lebih eksponen. Jika kamu membagi dua bilangan eksponen dengan basis yang sama, sama artinya dengan mengurangi pangkatnya. Simak bentuk pengurangan pangkat berikut ini.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"512\" height=\"328\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-14.png\" alt=\"\" class=\"wp-image-317878\" style=\"width:120px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Contohnya, 2<sup>9<\/sup>\/2<sup>3<\/sup> = 2<sup>9-3<\/sup> = 2<sup>6<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apabila nilai <em>m <\/em>= <em>n<\/em>, maka hasilnya pasti sama dengan satu. Apa benar demikian? Buat PR, ya!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Operasi Perkalian Pangkat<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Perkalian antarpangkat bilangan eksponen berlaku jika kamu memangkatkan suatu bilangan eksponen. Bingung? Yuk, simak bentuk perkaliannya.<\/p>\n\n\n\n(a<sup>m<\/sup>)<sup>n<\/sup> = a<sup>m x x<\/sup> = a<sup>mn<\/sup>, dengan syarat a \u2260 0 (basis tidak boleh sama dengan nol)\n\n\n\n<p class=\"wp-block-paragraph\">Contoh, (3<sup>4<\/sup>)<sup>2<\/sup> = 3<sup>4 \u00d7 2<\/sup> = 3<sup>8<\/sup><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Operasi Pembagian Pangkat<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Jika operasi perkalian pangkat bisa diperoleh dengan mempangkatkan bilangan ekponen, lalu bagaimana dengan sifat operasi pembagian ya? Pembagian pangkat pada bilangan eksponen merupakan bentuk lain dari bilangan yang diakarkan. Penasaran? Yuk, simak berikut ini.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"252\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-15.png\" alt=\"\" class=\"wp-image-317882\" style=\"width:120px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari bentuk di atas, Quipperian bisa tahu jika bilangan yang diakarkan itu sebenarnya bilangan eksponen yang pangkatnya berupa pecahan.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Pangkat Nol<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ada kalanya Quipperian menjumpai bentuk bilangan eksponen yang berpangkat nol. Lalu, apa arti pangkat nol itu? Ingat ya, berapapun bilangan jika dipangkatkan nol, maka hasilnya sama dengan satu. Adapun bentuk pangkat nol adalah a<sup>0<\/sup> = 1, dengan syarat a \u2260 0. Contoh 2<sup>0<\/sup> = 1, 1.000<sup>0<\/sup> = 1, 3<sup>0<\/sup> = 1, dan seterusnya.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Pangkat Bilangan Negatif<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, bagaimana bentuk penyelesaian bilangan eksponen yang pangkatnya berupa bilangan bulat negatif? Bentuk perpangkatan dengan bilangan bulat negatif adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"333\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-16.png\" alt=\"\" class=\"wp-image-317885\" style=\"width:100px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">dengan syarat basis tidak boleh sama dengan nol (<em>a<\/em> \u2260 0)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari bentuk di atas, diketahui bahwa bilangan eksponen dengan pangkat bilangan bulat negatif merupakan kebalikan atau invers dari bilangan eksponen pangkat positifnya. Bagaimana tahu jika keduanya saling berkebalikan? Hasil perkalian antara keduanya sama dengan satu.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Sifat Pangkat Satu<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Jika suatu bilangan dipangkatkan satu, hasilnya pasti sama dengan bilangan itu sendiri. Itu artinya, berapapun basisnya jika pangkatnya satu pasti hasilnya basis itu sendiri. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"494\" height=\"512\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-17.png\" alt=\"\" class=\"wp-image-317888\" style=\"width:120px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bagaimana Quipperian? Mudah, kan?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Penerapan Sifat-Sifat Eksponen<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Dalam kehidupan sehari-hari, sifat-sifat eksponen bisa dimanfaatkan untuk menyelesaikan berbagai permasalahan, contohnya seperti berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apakah Quipperian masih ingat, berapa kecepatan cahaya itu? Ya, benar sekali 300.000.000 m\/s. Oleh karena kecepatannya cukup tinggi, maka kecepatan cahaya biasa dinyatakan dalam bentuk notasi ilmiah, yaitu 3 \u00d7 10<sup>8<\/sup> m\/s. Jika ada benda lain selain cahaya yang kecepatannya 3 \u00d7 10<sup>4<\/sup> m\/s, berapa perbandingan antara kecepatan cahaya dan kecepatan benda tersebut? Pada perbandingan ini, berlaku sifat operasi pengurangan pangkat ya.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"133\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2024\/02\/unnamed-18.png\" alt=\"\" class=\"wp-image-317892\" style=\"width:180px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, perbandingan kecepatan cahaya dan kecepatan benda tersebut adalah 10<sup>4<\/sup>. Ternyata, dengan adanya sifat-sifat eksponen, kamu bisa lebih mudah menyelesaiakan soal-soal seperti contoh di atas ya.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Contoh Soal Sifat-Sifat Eksponen<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mengasah pemahamanmu tentang pembahasan kali ini, yuk simak beberapa contoh soal berikut ini.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Contoh Soal 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah toples memiliki ukuran panjang 25 cm dan lebar 5 cm. Berapakah luas toples tersebut dalam satuan km menggunakan sifat-sifat eksponen?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>PEMBAHASAN<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>p<\/em> = 25 cm = 25 \u00d7 10<sup>-5<\/sup> km<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>l<\/em> = 5 cm = 5 \u00d7 10<sup>-5<\/sup> km<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: <em>L<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawab:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari luas toples, gunakan persamaan luas persegipanjang ya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/tDpgVxF7C3WR7EiQzF07gdruUEaNNGBqYGNGzpJQ10-dNd8JnjRcAYlyGIAudakN7SnuD8l3GPpnbfntZ5DNRez_JIRGlCEAaWPlTMT8O48crOetca5gcswd7CxNnAq2QLj0ytJt3HBxogd_dgFq3g\" alt=\"\" style=\"width:180px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Perhitungan di atas menunjukkan bahwa luas toples bisa dicari dengan sifat operasi penjumlahan pangkat. Sebelum mengoperasikan pangkat, tentukan dahulu bilangan-bilangan yang memiliki basis sama. Selanjutnya, operasikan pangkatnya sesuai sifat-sifat eksponen yang berlaku.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, luas toples dalam satuan km adalah 5<sup>3<\/sup> \u00d7 10<sup>-10<\/sup> km.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Contoh Soal 2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Berapakah hasil dari 3<sup>4040<\/sup> + 9<sup>2020<\/sup>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk menyelesaikan soal tersebut, gunakan sifat-sifat eksponen, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lakukan modifikasi kedua bilangan sedemikian sehingga keduanya memiliki basis dan pangkat yang sama seperti berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3<sup>4040<\/sup> + 9<sup>2020<\/sup> = 3<sup>4040<\/sup> + (3<sup>2<\/sup>)<sup>2020<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 3<sup>4040<\/sup> + 3<sup>4040<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 2 \u00d7\u00a0 3<sup>4040<\/sup>Jadi, hasil dari 3<sup>4040<\/sup> + 9<sup>2020<\/sup> adalah 2 \u00d7\u00a0 3<sup>4040<\/sup>.<\/p>\n\n\n\n<hr\/>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog tentang sifat-sifat eksponen. Semoga bermanfaat, ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sumber:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/sumberbelajar.seamolec.org\/Media\/Dokumen\/59c1c6b6865eacac04e3cd2a\/a781043c86f730ae8834c4a52dd61f8f.pdf\">https:\/\/sumberbelajar.seamolec.org\/Media\/Dokumen\/59c1c6b6865eacac04e3cd2a\/a781043c86f730ae8834c4a52dd61f8f.pdf<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/eksponen\">https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/eksponen<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat dan tetap semangat, ya. Apakah Quipperian sudah pernah belajar tentang bilangan eksponen? Tahukah kamu jika keberadaan eksponen&hellip;<\/p>\n","protected":false},"author":156446345,"featured_media":317867,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[],"ppma_author":[679386822],"class_list":["post-317866","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Sifat Eksponen - Pengertian, Sifat, Penerapan, dan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Apakah Quipperian sudah pernah belajar tentang bilangan eksponen? 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