{"id":115314,"date":"2020-01-29T18:20:44","date_gmt":"2020-01-29T17:20:44","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/aritmetica\/potenciacion.html"},"modified":"2026-10-06T18:44:46","modified_gmt":"2026-10-06T16:44:46","slug":"potenciacion","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\/potenciacion.html","title":{"rendered":"Potenciaci\u00f3n"},"content":{"rendered":"<section style=\"\">\r\n          \n\n<p class=\"wp-block-paragraph\">La <span><strong>potenciaci\u00f3n<\/strong><\/span> es una forma abreviada de escribir un <strong>producto<\/strong> formado por varios <strong>factores iguales<\/strong>.<\/p>\n\n\r\n                          \n\n<p class=\"wp-block-paragraph\"><strong>7  \u00b7 7 \u00b7 7 \u00b7 7 = <span id=\"exponente\">7<sup>4<\/sup><\/span> <\/strong><\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">Base<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">La <strong>base<\/strong> de una <strong>potencia<\/strong> es el <strong>n\u00famero<\/strong> que <strong>multiplicamos<\/strong> por s\u00ed mismo, en este caso el 7. <\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">Exponente<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">El <strong>exponente<\/strong> de una <strong>potencia<\/strong> indica el <strong>n\u00famero<\/strong> de veces que <strong>multiplicamos<\/strong> la <strong>base<\/strong>, en el ejemplo es el 4.<\/p>\n\n\r\n                             \r\n\r\n              \n\n<h2 class=\"wp-block-heading\">Potencias de exponente natural<\/h2>\n\n\r\n                         \r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">1. <\/h2>\n\n<strong>Un n\u00famero elevado a 0 es igual a 1.<\/strong><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>a<sup>0<\/sup> = 1 <\/strong><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\" >6<sup>0<\/sup> = 1<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">2. <\/h2>\n\n<strong>Un n\u00famero elevado a 1 es igual a s\u00ed mismo.<\/strong><\/p>\n\n\r\n                          \n\n<p class=\"wp-block-paragraph\"><strong>a<sup>1<\/sup> = a<\/strong><\/p>\n\n\r\n                          \n\n<p class=\"wp-block-paragraph\">6<sup>1<\/sup> = 6<\/p>\n\n\r\n                          \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">3. <\/h2>\n\n<strong>Producto de potencias con la misma base<\/strong>: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Es otra <strong>potencia<\/strong> con <strong>la misma base<\/strong> y cuyo <strong>exponente<\/strong> es la <strong>suma de los exponentes<\/strong>.<\/p>\n\n\r\n                            \r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>a<sup>m<\/sup> \u00b7 a <sup>n <\/sup> = a<sup>m+n<\/sup><\/strong><\/p>\n\n\r\n                            \r\n                            \n\n<p class=\"wp-block-paragraph\">3<sup>5 <\/sup> \u00b7 3<sup>2 <\/sup> = 3<sup>5+2 <\/sup> = 3<sup>7<\/sup><\/p>\n\n\r\n                            \r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">4. <\/h2>\n\n<strong>Divisi\u00f3n de potencias con la misma base<\/strong>: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Es otra <strong>potencia<\/strong> con la <strong>misma base<\/strong> y cuyo <strong>exponente<\/strong> es la <strong>diferencia de los exponentes<\/strong>.<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"> <strong>a<sup>m <\/sup> : a <sup>n <\/sup> = a<sup>m - n<\/sup><\/strong><\/p>\n\n \r\n                            \n\n<p class=\"wp-block-paragraph\">3<sup>5 <\/sup> : 3<sup>2 <\/sup> = 3<sup>5 - 2 <\/sup>= 3<sup>3<\/sup> <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">5. <\/h2>\n\n<strong>Potencia de una potencia<\/strong>: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Es otra <strong>potencia<\/strong> con la <strong>misma base<\/strong> y cuyo exponente es el <strong>producto de los exponentes<\/strong>.<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>(a<sup>m<\/sup>)<sup>n<\/sup> = a<sup>m \u00b7 n <\/sup><\/strong> <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">(3<sup>5<\/sup>)<sup>3<\/sup> = 3<sup>15<\/sup> <\/p>\n\n\t\t\t       \r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">6. <\/h2>\n\n<strong>Producto de potencias con el mismo exponente<\/strong>: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Es otra <strong>potencia<\/strong> con el <strong>mismo exponente<\/strong> y cuya <strong>base<\/strong> es el <strong>producto de las bases<\/strong>. <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>a<sup>n <\/sup> \u00b7 b <sup>n <\/sup> = (a \u00b7 b) <sup>n<\/sup><\/strong><\/p>\n\n\r\n                            \r\n                            \n\n<p class=\"wp-block-paragraph\">2<sup>5 <\/sup> \u00b7 4<sup>5 <\/sup> = 8<sup>5<\/sup><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">7. <\/h2>\n\n<strong>Cociente  de potencias con el mismo exponente<\/strong>: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Es otra <strong>potencia<\/strong> con el <strong>mismo exponente<\/strong> y cuya <strong>base<\/strong> es el <strong>cociente de  las bases<\/strong>.<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>a<sup>n <\/sup> : b<sup>n <\/sup> = (a : b)<sup>n<\/sup><\/strong><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">6<sup>4 <\/sup> : 3<sup>4 <\/sup> = 2<sup>4<\/sup><\/p>\n\n\r\n                                \r\n\r\n                          \n\n<h2 class=\"wp-block-heading\">Signo de una potencia de base entera<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Para determinar el <strong>signo<\/strong> de la <strong>potencia de un n\u00famero entero <\/strong>tendremos en cuenta que:<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"> \n\n<h2 class=\"wp-block-heading\">1.<\/h2>\n\n Las <strong>potencias de exponente par<\/strong> son siempre <strong>positivas<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-1.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 1\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">2<sup>6<\/sup> = 64<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">(\u22122)<sup>6<\/sup> = 64<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"> \n\n<h2 class=\"wp-block-heading\">2.<\/h2>\n\n Las <strong>potencias de exponente  impar<\/strong> tiene el <strong>mismo signo<\/strong> de la <strong>base<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-2.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 2\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">2<sup>3<\/sup> =  8 <\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">(\u22122)<sup>3<\/sup> =  \u22128<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Potencias de exponente negativo<\/h3>\n\n\r\n                        \n\n<p  class=\"wp-block-paragraph\">La <strong>potencia<\/strong> de un <strong>n\u00famero entero<\/strong> con  <strong>exponente negativo<\/strong> es igual al <strong>inverso del n\u00famero<\/strong> elevado a <strong>exponente positivo<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-3.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 3\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-4.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 4\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-5.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 5\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-6.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 6\"  ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Potencias de fracciones<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Para elevar una <strong>fracci\u00f3n<\/strong> a una <strong>potencia<\/strong> se eleva tanto el <strong>numerador<\/strong> como el <strong>denominador<\/strong> al <strong>exponente<\/strong>.<\/p>\n\n\r\n                          \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-7.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 7\"  ><\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-8.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 8\"  ><\/p>\n\n\r\n                        \r\n\t  \t\t  \t\t\t \n\n<h3 class=\"wp-block-heading\">Potencias fraccionarias de exponente negativo<\/h3>\n\n\r\n                         \n\n<p class=\"wp-block-paragraph\">Una <strong>potencia fraccionaria<\/strong> de <strong>exponente negativo<\/strong> es igual a la <strong>inversa de la fracci\u00f3n<\/strong> elevada a <strong>exponente positivo<\/strong>.<\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-9.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 9\"  ><\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-10.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 10\"  ><\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-11.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 11\"  ><\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-12.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 12\"  ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Potencias de exponente fraccionario<\/h3>\n\n\r\n                        \r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-13.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 13\"  ><\/p>\n\n\r\n                         \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-14.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 14\"  ><\/p>\n\n\r\n                        \n\n<h3 class=\"wp-block-heading\">Potencias de exponente fraccionario y negativo<\/h3>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-15.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 15\"  ><\/p>\n\n\r\n                         \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/potenciaci&oacute;n-16.gif\" alt=\"Explicaciones y ejemplos de potenciaci&oacute;n - 16\"  ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/>\r\n            \r\n            <\/section><\/p>\n","protected":false},"excerpt":{"rendered":"<p>La potenciaci\u00f3n es una forma abreviada de escribir un producto formado por varios factores iguales. 7 \u00b7 7 \u00b7 7 \u00b7 7 = 74 Base La base de una potencia es el n\u00famero que multiplicamos por s\u00ed mismo, en este caso el 7. Exponente El exponente de una potencia indica el n\u00famero de veces que [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[377],"tags":[363],"class_list":["post-115314","post","type-post","status-publish","format-standard","hentry","category-aritmetica","tag-p"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">p<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">p<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 7 a\u00f1os hace","modified":"Actualizado 2 semanas hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 6 octubre 2026"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 20 min","modified":"Actualizado el 6 octubre 2026 18 h 44 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=115314"}],"version-history":[{"count":5,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115314\/revisions"}],"predecessor-version":[{"id":140080,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115314\/revisions\/140080"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=115314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=115314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=115314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}