[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571807-105":53,"doc-detail-571807-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","properties-of-exponents","Properties of Exponents","","Properties of exponents explains what exponents (powers or degrees) mean by describing how a base is multiplied by itself repeatedly. It introduces key exponent rules, including the product rule, quotient rule, and two power rules, with general forms and applications. The notes also cover negative exponents, including how to flip the expression and change the sign, and the zero exponent rule where any nonzero base equals one. It emphasizes that exponent rules require the same base.",{"@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/properties-of-exponents/571807/",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/properties-of-exponents/571807.png","ImageObject",442,249,{"name":88,"@type":89},"jay","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",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What does an exponent tell you about a base?","Question",{"text":109,"@type":110},"An exponent shows how many times the base is multiplied by itself. For example, a variable to the fifth power means it is multiplied by itself five times.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"Which rules apply when you multiply or divide powers with the same base?",{"text":114,"@type":110},"For the same base, the product rule adds exponents and the quotient rule subtracts exponents. These simplifications only work when the bases are the same.",{"name":116,"@type":107,"acceptedAnswer":117},"How do negative exponents and zero exponents work?",{"text":118,"@type":110},"Negative exponents are handled by flipping the fraction and making the exponent positive. Zero exponents make any nonzero base equal to one.","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},571807,1792020289,{"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":73,"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":9},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Properties of Exponents  \nAn exponent (also called power or degree) tells us how many times the base will be multiplied by itself. For example 􀀁 􀀂, the exponent is 5 and the base is 􀀁 . This means that the variable 􀀁 will be multiplied by itself 5 times. You can also think of this as 􀀁 to the fifth power.  \nBelow is a list of properties of exponents:  \n\n| Properties | General Form | Application | Example |\n| --- | --- | --- | --- |\n| Product Rule\u003Cbr>Same base add exponents | 􀀄 􀀅􀀃 􀀃 | 􀀃􀀄􀀆􀀅 | 􀀁 􀀂 􀀁 􀀇 􀀈 􀀁 􀀂􀀆􀀇 􀀈 􀀁 􀀉 |\n| Quotient Rule\u003Cbr>Same base subtract exponents | 􀀃􀀄\u003Cbr>􀀃􀀅 | 􀀃􀀄􀀊􀀅 | 􀀋\u003Cbr>􀀁\u003Cbr>􀀋􀀊􀀂 􀀌\u003Cbr> 􀀂 􀀈 􀀁 􀀈 􀀁\u003Cbr>􀀁 |\n| Power Rule I\u003Cbr>Power raised to a power multiply exponents. | 􀀍􀀃􀀄 􀀎 􀀅 | 􀀃􀀄􀀅 | 􀀍􀀁 􀀇 􀀎 􀀌 􀀈 􀀁 􀀇􀀏􀀌 􀀈 􀀁 􀀐􀀑 |\n| Power Rule II\u003Cbr>Product to power distribute to each base | 􀀍􀀃􀀒􀀎 􀀄 | 􀀄 􀀅􀀃 􀀃 | 􀀍􀀓􀀁 􀀇 􀀎 􀀑 􀀈 􀀓 􀀑 􀀁 􀀇􀀏􀀑 􀀈 􀀔􀀕􀀁 􀀖 |\n| Negative Exponent I\u003Cbr>Flip and change sign to positive | 􀀃 􀀊􀀄 | 􀀔\u003Cbr>􀀃􀀄 | 􀀔􀀊􀀇\u003Cbr>􀀁 􀀈 ~~ ~~􀀁 􀀇 |\n| Negative Exponent II\u003Cbr>Flip and change sign to positive | 􀀔\u003Cbr>􀀃 􀀊􀀄 | 􀀃􀀄 | 􀀔\u003Cbr>􀀂  􀀊􀀂 􀀈 􀀁􀀁 |\n| Zero Exponent\u003Cbr>Anything to the zero power (except 0) is one | 􀀃 􀀗 | 􀀃 􀀗 􀀈 􀀔 | 􀀍􀀘􀀓􀀁􀀎 􀀗 􀀈 􀀔 |\n\n• It is important to note that none of these applications can occur if the bases are not the same.  \n􀀚  \nFor example, 􀀙  cannot be simplified.  \n􀀛 􀀜  \nUsing a Combination of Rules  \nAt one point, you may be asked to use a combination of these properties.  \nExample:  \n􀀝􀀑 􀀜 􀀛 􀀞 􀀟 􀀚  \n•  \n•  \n􀀑􀀠􀀡 􀀛 􀀠􀀢  \n•  \n􀀑􀀠􀀚 􀀛 􀀠􀀡  \n􀀑􀀠􀀡 􀀛 􀀠􀀢  \n• 􀀤 􀀐􀀂􀀊􀀐􀀗 􀀥 􀀐􀀗􀀊􀀐􀀖  \n• 􀀤 􀀂 􀀥 􀀊􀀖  \n􀀣 Power Rule  \n􀀣 Quotient Rule  \n􀀣 Negative Exponent  \n􀀇􀀑  \n• ~~ ~~  \n􀀛 􀀢  \nExample:  \n• 􀀦􀀧􀀫􀀨􀀨􀀩􀀜􀀪~~ ~~ 􀀬 􀀊􀀇 􀀣 Power Rule  \n􀀨􀀩􀀏􀀨􀀜 􀀠􀀏􀀨􀀜  \n• 􀀧~~ ~~􀀫~~ ~~􀀨􀀜􀀏􀀜~~ ~~ Note: When a base does not have an exponent there is really a one as the  \npower. So that, 􀀭 is understood as 􀀭 􀀐  \n􀀠􀀞 􀀨􀀜  \n• 􀀧~~ ~~􀀫􀀪􀀮~~ ~~ 􀀣 Negative Exponents  \n􀀠􀀞  \n•  􀀧   \n􀀪 􀀜 􀀫 􀀮","cbCairo7QHnhTJIW","https://ap.wps.com/l/cbCairo7QHnhTJIW","pdf",81508,"English","# Properties of Exponents\n## Definition of Exponents\n## List of Exponent Properties\n### Product Rule and Quotient Rule\n### Power Rule I and II\n### Negative Exponents I and II\n### Zero Exponent\n## Using a Combination of Rules\n## Note on Same Bases","[{\"question\":\"What does an exponent tell you about a base?\",\"answer\":\"An exponent shows how many times the base is multiplied by itself. For example, a variable to the fifth power means it is multiplied by itself five times.\"},{\"question\":\"Which rules apply when you multiply or divide powers with the same base?\",\"answer\":\"For the same base, the product rule adds exponents and the quotient rule subtracts exponents. These simplifications only work when the bases are the same.\"},{\"question\":\"How do negative exponents and zero exponents work?\",\"answer\":\"Negative exponents are handled by flipping the fraction and making the exponent positive. Zero exponents make any nonzero base equal to one.\"}]","Properties of Exponents | PDF",1791923792]