[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-398510-105":59,"doc-detail-398510-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","division-property-of-exponents-practice-problems","Division Property of Exponents - Practice Problems","","Division Property of Exponents练习讲义围绕同底数幂的除法运算规则展开，强调保留底数并相减指数；同时给出商的幂应当同时作用于分子与分母的处理方法。内容包含快速复习要点、提示与分步示例，要求将变量与系数分别简化，并通过多道化简题与文字题（如长方形面积与宽度求长度、均分颗粒与袋数、已知体积与底面积求高度）训练指数表达式的化简能力。",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/division-property-of-exponents-practice-problems/398510/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/division-property-of-exponents-practice-problems/398510.png","ImageObject",300,407,{"name":92,"@type":93},"lugxt","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-08","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you simplify a quotient of powers with the same base?","Question",{"text":113,"@type":114},"Keep the common base and subtract the exponents to get the new exponent (for x≠0).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What happens when a quotient is raised to a power?",{"text":118,"@type":114},"The power applies to both the numerator and the denominator, so you treat the top and bottom using the quotient’s exponent rules.",{"name":120,"@type":111,"acceptedAnswer":121},"Why should coefficients and variables be handled separately?",{"text":122,"@type":114},"Coefficients combine by ordinary arithmetic, while variables follow the exponent rules, allowing the expression to simplify cleanly to the final power form.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},398510,1791235325,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},3985747862600,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Practice 􀀏 Progress 􀀏 Succeed | TSIA2 Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nDivision Property of Exponents  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nWhen you divide powers with the same base, keep the base and subtract the exponents: xxab~~ ~~ = xa􀀀b (for x  0) . When a quotient is raised to a power, the power applies to top and bottom: 􀀒 xy􀀓 a = ~~ ~~xyaa . Divide the number coef􀀂cients separately from the variables.  \n7  \n▷ Example: Simplify xx3 . Work: The base x is the same on top and bottom, so keep the base and subtract  \nthe exponents: 7 − 3 = 4 . ⋆ Answer: x4  \n♦ Practice Problems  \nSimplify each quotient. Assume no variable equals zero.  \n♦ Word Problems  \n15. A rectangle has area x9 square units and width x4 units. Its length is area divided by width. Write the length as a power of x.  \n16. A jar holds 108 tiny grains, split equally among 102 bags. How many grains per bag? Write the answer as a power of 10.  \n17. The volume of a box is 24y7 and its base area is 6y3 . The height is volume divided by base area. Find the height.  \n6 a6  \n18. A design 􀀂le scales both the width and height by the same factor a . The ratio includes a6 . Simplify the ratio factor.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | TSIA2 Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1. x4  \n2. y4 3. 25  \n4. a9 5. 1  \n6.  3x5   \n7. x5 y3 13. x6  \nx3  14. 63  \n8.  \ny3 15. x5  \n9. 3a2 16. 106  \n10. b5 17. 4y4  \n 11. 5 18. 1  \n12. p3 q5  \nStep-by-Step Explanations  \n1. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Dividing powers of the same base cancels matching factors, so you subtract the exponents: 6 􀀀 2 = 4, giving x4 . So the 􀀂nal answer is x4 .  \n2. A good way to think about this is: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Subtract the exponents: 9 􀀀 5 = 4, so y4 . So the 􀀂nal answer is y4 .  \n3. Step by step: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Keep the base 2 and subtract: 8 􀀀 3 = 5, so 25 (which is 32) . So the 􀀂nal answer is 25 .  \n4. Take it one move at a time: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is The lone a is a1 , so 10 􀀀 1 = 9, giving a9 . So the 􀀂nal answer is a9 .  \n5. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Equal exponents subtract to 0, and m0 = 1 – any quantity divi","cbCaicFo9BWE4Y3v","https://ap.wps.com/l/cbCaicFo9BWE4Y3v","pdf",116854,"English","# Quick Review and Helpful Hints\n## Division property rule when dividing powers\n## Raising a quotient to a power\n## Separate coefficients and variables\n# Example and Practice Problems\n## Simplify each quotient\n## Word problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"How do you simplify a quotient of powers with the same base?\",\"answer\":\"Keep the common base and subtract the exponents to get the new exponent (for x≠0).\"},{\"question\":\"What happens when a quotient is raised to a power?\",\"answer\":\"The power applies to both the numerator and the denominator, so you treat the top and bottom using the quotient’s exponent rules.\"},{\"question\":\"Why should coefficients and variables be handled separately?\",\"answer\":\"Coefficients combine by ordinary arithmetic, while variables follow the exponent rules, allowing the expression to simplify cleanly to the final power form.\"}]","Division Property of Exponents - Practice Problems | PDF",1790482715]