{"id":214,"date":"2026-03-05T11:29:42","date_gmt":"2026-03-05T10:29:42","guid":{"rendered":"https:\/\/zalapto.pl\/baza\/?p=214"},"modified":"2026-03-05T11:31:32","modified_gmt":"2026-03-05T10:31:32","slug":"zadanie-3-matura-probna-matematyka-marzec-2026","status":"publish","type":"post","link":"https:\/\/zalapto.pl\/baza\/zadanie-3-matura-probna-matematyka-marzec-2026\/","title":{"rendered":"Zadanie 3 &#8211; Matura pr\u00f3bna matematyka CKE (Marzec 2026)"},"content":{"rendered":"\n\n\n<div class=\"mb-4\">\n    <a href=\"https:\/\/zalapto.pl\/baza\/matura-probna-matematyka-cke-2026-marzec\" class=\"btn btn-outline-primary btn-sm rounded-pill fw-bold shadow-sm\">\n        <i class=\"bi bi-arrow-left me-1\"><\/i> Wr\u00f3\u0107 do pe\u0142nego arkusza z marcem 2026\n    <\/a>\n<\/div>\n\n<div class=\"card border border-light shadow-sm rounded-4 mb-5\">\n    <div class=\"card-body p-4 p-md-5\">\n        \n        <h2 class=\"fw-bold text-dark mb-4 border-bottom pb-2 fs-4\">Tre\u015b\u0107 zadania<\/h2>\n        <div class=\"fs-5 mb-4 text-dark\" style=\"line-height: 1.8;\">\n            Doko\u0144cz zdanie. Wybierz w\u0142a\u015bciw\u0105 odpowied\u017a spo\u015br\u00f3d podanych.<br><br>\n            Liczba \\( \\frac{3^{10}\\cdot9^{20}}{27^{15}} \\) jest r\u00f3wna:<br>\n            A. \\( 1 \\)<br>\n            B. \\( 3^5 \\)<br>\n            C. \\( 3^{15} \\)<br>\n            D. \\( 3^{45} \\)\n        <\/div>\n\n        <h2 class=\"fw-bold text-dark mb-4 border-bottom pb-2 mt-5 fs-4\">Rozwi\u0105zanie krok po kroku<\/h2>\n        \n        <details class=\"mb-3\">\n            <summary class=\"btn btn-warning text-dark fw-bold rounded-pill px-4\" style=\"cursor: pointer;\">\n                <i class=\"bi bi-lightbulb\"><\/i> Zobacz podpowied\u017a\n            <\/summary>\n            <div class=\"p-4 mt-3 bg-light border rounded-4\">\n                Aby m\u00f3c dzia\u0142a\u0107 na pot\u0119gach, musisz sprowadzi\u0107 wszystkie liczby do wsp\u00f3lnej podstawy. Zauwa\u017c, \u017ce \\( 9 \\) to to samo co \\( 3^2 \\), a \\( 27 \\) to \\( 3^3 \\). U\u017cyj wzor\u00f3w na pot\u0119gowanie pot\u0119gi oraz mno\u017cenie i dzielenie pot\u0119g o tych samych podstawach.\n            <\/div>\n        <\/details>\n\n        <details>\n            <summary class=\"btn btn-success fw-bold rounded-pill px-4\" style=\"cursor: pointer;\">\n                <i class=\"bi bi-check-circle\"><\/i> Sprawd\u017a pe\u0142ne rozwi\u0105zanie\n            <\/summary>\n            <div class=\"p-4 mt-3 bg-success bg-opacity-10 border border-success rounded-4 text-dark fs-6\">\n                \n                <p><strong>1. Zamieniamy podstawy na pot\u0119gi liczby 3:<\/strong><\/p>\n                Korzystaj\u0105c ze wzoru \\( (a^m)^n = a^{m \\cdot n} \\), rozpiszmy sobie liczby 9 oraz 27:\n                $$ 9^{20} = (3^2)^{20} = 3^{2 \\cdot 20} = 3^{40} $$\n                $$ 27^{15} = (3^3)^{15} = 3^{3 \\cdot 15} = 3^{45} $$\n                \n                <p><strong>2. Wstawiamy nowe liczby do u\u0142amka:<\/strong><\/p>\n                <div class=\"za-math-scroll\">\n                    $$ \\frac{3^{10} \\cdot 3^{40}}{3^{45}} $$\n                <\/div>\n\n                <p><strong>3. Obliczamy u\u017cywaj\u0105c praw dzia\u0142a\u0144 na pot\u0119gach:<\/strong><\/p>\n                Przy mno\u017ceniu wykladniki dodajemy, a przy dzieleniu (kreska u\u0142amkowa) odejmujemy:\n                $$ = \\frac{3^{10 + 40}}{3^{45}} = \\frac{3^{50}}{3^{45}} $$\n                $$ = 3^{50 &#8211; 45} = 3^5 $$\n                \n                <hr class=\"border-success opacity-25 my-4\">\n                <p class=\"fw-bold mb-0 text-success fs-5\">Poprawna odpowied\u017a: B<\/p>\n                \n            <\/div>\n        <\/details>\n\n    <\/div>\n<\/div>\n\n<div class=\"bg-primary bg-opacity-10 border border-primary border-opacity-25 rounded-4 p-4 text-center mt-2\">\n    <p class=\"fw-bold text-primary mb-2\">To zadanie sprawi\u0142o Ci trudno\u015b\u0107?<\/p>\n    <p class=\"small text-muted mb-3\">Zosta\u0142o ma\u0142o czasu do maja, ale z nami na pewno to <strong>Za\u0142apiesz<\/strong>. Przer\u00f3bmy to razem na wirtualnej tablicy.<\/p>\n    <a href=\"https:\/\/zalapto.pl\/#zapisy\" class=\"btn btn-primary btn-sm rounded-pill fw-bold px-4\">Zapisz si\u0119 na korepetycje<\/a>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Wr\u00f3\u0107 do pe\u0142nego arkusza z marcem 2026 Tre\u015b\u0107 zadania Doko\u0144cz zdanie. Wybierz w\u0142a\u015bciw\u0105 odpowied\u017a spo\u015br\u00f3d podanych. Liczba \\( \\frac{3^{10}\\cdot9^{20}}{27^{15}} \\) jest r\u00f3wna: A. \\( 1 \\) B. \\( 3^5 \\) C. \\( 3^{15} \\) D. \\( 3^{45} \\) Rozwi\u0105zanie krok po kroku Zobacz podpowied\u017a Aby m\u00f3c dzia\u0142a\u0107 na pot\u0119gach, musisz sprowadzi\u0107 wszystkie liczby do wsp\u00f3lnej [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,26],"tags":[],"class_list":["post-214","post","type-post","status-publish","format-standard","hentry","category-matura-podstawowa","category-zadania"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/214","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/comments?post=214"}],"version-history":[{"count":1,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/214\/revisions"}],"predecessor-version":[{"id":215,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/214\/revisions\/215"}],"wp:attachment":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/media?parent=214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/categories?post=214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/tags?post=214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}