[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571810-105":53,"doc-detail-571810-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","exponent-properties-a-comprehensive-educational-guide","Exponent Properties - A Comprehensive Educational Guide","","This document provides a clear and concise overview of the fundamental mathematical laws governing exponents. It systematically details the seven essential properties: product of like bases, quotient of like bases, power to a power, product to a power, quotient to a power, the zero exponent rule, and the negative exponent rule. Each property is explained with its corresponding algebraic formula and an intuitive description of the underlying operation. Designed for students and educators alike, the material serves as a practical reference for simplifying complex exponential expressions through clear, standardized algebraic steps. By presenting both the theoretical rule and the operational logic—such as 'adding exponents for multiplication' or 'switching floors for negative exponents'—the document reinforces algebraic fluency and computational accuracy, making it an indispensable tool for mathematics study and review.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/exponent-properties-a-comprehensive-educational-guide/571810/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/exponent-properties-a-comprehensive-educational-guide/571810.png","ImageObject",442,249,{"name":88,"@type":89},"WPS_1790064749","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-25","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",7,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"How do you simplify the product of two powers with the same base?","Question",{"text":109,"@type":110},"To multiply powers with the same base, you add the exponents together while keeping the base unchanged, as expressed in the formula a^m * a^n = a^(m+n).","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What is the result of any non-zero number raised to the zero power?",{"text":114,"@type":110},"Any number raised to the power of zero is always equal to 1.",{"name":116,"@type":107,"acceptedAnswer":117},"How are negative exponents handled in algebraic expressions?",{"text":118,"@type":110},"Negative exponents are made positive by taking the reciprocal of the base and the exponent, effectively moving the base-exponent pair to the opposite side of the fraction bar, a process often described as 'switching floors'.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571810,1792019208,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":4},3985747859154,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Exponent Properties  \n1. Product of like bases: aman 􀀠 am􀀎n  \nTo multiply powers with the same base, add the exponents and keep the common base.  \nExample:  \nam  \n2. Quotient of like bases: an 􀀠 am􀀐n  \nTo divide powers with the same base, subtract the exponents and keep the common base.  \nExample: ~~ ~~  \n3. Power to a power: (am ) n 􀀠 amn To raise a power to a power, keep the base and multiply the exponents.  \nExample:  \n4. Product to a power: (ab)m 􀀠 ambm  \nTo raise a product to a power, raise each factor to the power.  \nExample:  \n5. Quotient to a power 􀂧􀂨 a  􀂷􀂸 n 􀀠 an   \n􀂩b 􀂹 bn  \nTo raise a quotient to a power, raise the numerator and the denominator to the power. Example: ( ) ~~ ~~  \n6. Zero Exponent: a 0 􀀠 1  \nAny number raised to the zero power is equal to “1”.  \nExamples:  \n 1   \n7. Negative exponent: a 􀀐n 􀀠 an  \nUnhappy (negative) exponents will become happy (positive) by having the base/exponent pair “switch floors”. Another way to interpret this: negative exponents mean to write the reciprocal of the original, making the exponent positive.  \nExamples: ~~ ~~ ~~ ~~ ( ) ( ) ~~ ~~","cbCaicrAUcHZkXqm","https://ap.wps.com/l/cbCaicrAUcHZkXqm","pdf",200649,"English","# Exponent Properties\n## Product and Quotient Rules\n## Power Operations\n## Special Exponents","[{\"question\":\"How do you simplify the product of two powers with the same base?\",\"answer\":\"To multiply powers with the same base, you add the exponents together while keeping the base unchanged, as expressed in the formula a^m * a^n = a^(m+n).\"},{\"question\":\"What is the result of any non-zero number raised to the zero power?\",\"answer\":\"Any number raised to the power of zero is always equal to 1.\"},{\"question\":\"How are negative exponents handled in algebraic expressions?\",\"answer\":\"Negative exponents are made positive by taking the reciprocal of the base and the exponent, effectively moving the base-exponent pair to the opposite side of the fraction bar, a process often described as 'switching floors'.\"}]","Exponent Properties - A Comprehensive Educational Guide | PDF",1791923800]