[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-359064-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-359064-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","exponents-factors-roots-mixed-review-a","Exponents, Factors & Roots - Mixed Review (A)","","Mixed practice worksheet focused on exponents, exponential notation, evaluating powers, and applying order of operations involving exponents. Students complete items on converting expressions such as repeated multiplication and powers of 10, determining results for sums and differences with exponents, and using factor pairs, GCF, and LCM. Additional sections cover prime factorization in tree form and exponent form, plus square root estimation and interval placement. Includes a multi-part challenge involving packaging peaches and mangos into identical boxes and finding a square stall’s side length from its area.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/exponents-factors-roots-mixed-review-a/359064/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/exponents-factors-roots-mixed-review-a/359064.png","ImageObject",300,407,{"name":42,"@type":43},"Rhys","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",18,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you write a number like 4 × 4 × 4 × 4 in exponent form?","Question",{"text":63,"@type":64},"You rewrite the repeated multiplication as a base with an exponent equal to the number of factors. For 4 × 4 × 4 × 4, the result is 4^4.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the difference between GCF and LCM when working with factors?",{"text":68,"@type":64},"The GCF is the greatest number that divides both integers, while the LCM is the least common multiple shared by both. For example, GCF(42, 56) is 14 and LCM(8, 12) is 24.",{"name":70,"@type":61,"acceptedAnswer":71},"How can you estimate square roots like √50 or √75 to the nearest whole number?",{"text":72,"@type":64},"Compare the value to nearby perfect squares. √50 is closest to 49 (7), and √75 is closest to 81 (9), so the nearest whole-number approximations are 7 and 9 respectively.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},359064,1790218297,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":128,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":111,"preview_page_count":4},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Name:     \nExponents, Factors & Roots—Mixed Review (A)  \nDirections: Complete each section. Show your work.  \nSection 1: Exponents & Exponential Notation  \n1. In 73 , the base is   and the exponent is    \n2. Write 4 × 4 × 4 × 4 in exponent form = __________  \n3. Write 25 as repeated multiplication = __________________  \n4. True or False? 40 = 0 __________  \nSection 2: Evaluating Exponents & Powers of 10  \n5. 34 = ___________ 7. 103 = ___________  \n6. 26 = ___________ 8. 100 = ___________  \nSection 3: Order of Operations with Exponents  \n9. 2 + 32 =   11. 5 + 23 =    \n10. (4 + 1)2 =   12. 33 − (2 + 3)2 =    \nSection 4: Factors, GCF & LCM  \n13. List all factor pairs of 30:  \n17. LCM (4, 6) =    \n18. LCM (8, 12) =    \n19. GCF (42, 56) =    \n20. LCM (9, 15) =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nSection 5: Prime Factorization  \nComplete each prime factor tree and then write the prime factorization of each number.  \nA) B) C)  \n18 =   24 =   72 =    \nWrite the prime factorization of each number in exponent form:  \n21. 36 =   23. 60 =    \n22. 48 =   24. 100 =    \nSection 6: Square Roots  \n25. √20 is between   and    \n26. √50 ≈   (nearest whole number)  \n27. √75 ≈   (nearest whole number)  \n28. √20 is between   and    \n29. √50 ≈   (nearest whole number)  \n30. √75 ≈   (nearest whole number)  \n31. Challenge Problem  \nA market vendor has 36 peaches and 48 mangos to pack into identical gift boxes.  \nShe also wants to know the side length of her square stall, which has an area of 144 sq ft.  \na) What is the GCF of 36 and 48? What is the maximum number of boxes?    \nb) How many peaches and mangos go in each box?    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \nSection 1: Exponents & Exponential Notation 1.) → base = 7, exponent = 3 3.) → 2 × 2 × 2 × 2 × 2  \n2.) → 44 4.) → False (40 = 1)  \nSection 2: Evaluating Exponents & Powers of 10  \n5.) → 81 7.) → 1,000  \n6.) → 64 8.) → 1  \nSection 3: Order of Operations with Exponents  \n9.) 2 + 32 = 11  \n10.) (4 + 1)2 = 25  \n11.) 5 × 23 = 40  \n12.) 33 − (2 + 3)2 = 2  \nSection 4: Factors, GCF & LCM  \n13.) → 1×30, 2×15, 3×10, 5×6 17.) → 12  \n14.) → Prime 18.) → 24  \n15.) → 12 19.) → 14  \n16.) → 9 20.) → 45  \nSection 5: Prime Factorization  \nA) 18 = 2 × 3! B) 24 = 2\" × 3 C) 72 = 2\" × 3!  \n21.) 36 = 22 × 32  \n22.) 48 = 24 × 3  \n23.) 60 = 22 × 3 × 5  \n24.) 100 = 22 × 52  \nSection 6: Square Roots  \n25.) √49 → 7  \n26.) √144 → 12  \n27.) √225 → 15  \n28.) √20 → 4 and 5  \n29.) √50 ≈   (nearest whole number) → 7  \n30.) √75 ≈   (nearest whole number) → 9  \n31.) Challenge Problem:  \na) GCF(36, 48) = 12 boxes (factors of 36: 1,2,3,4,6,9,12,18,36; factors of 48: 1,2,3,4,6,8,12,16,24,48; GCF=12)  \nb) 3 apples and 4 oranges per box (36÷12=3 apples, 48÷12=4 oranges)  \nc) 12 feet (√144 = 12)  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaiaXMBNAGeql8","https://ap.wps.com/l/cbCaiaXMBNAGeql8","pdf",1593743,"English","# Exponents & Exponential Notation\n# Evaluating Exponents & Powers of 10\n# Order of Operations with Exponents\n# Factors, GCF & LCM\n# Prime Factorization\n# Square Roots\n## Challenge Problem","[{\"question\":\"How do you write a number like 4 × 4 × 4 × 4 in exponent form?\",\"answer\":\"You rewrite the repeated multiplication as a base with an exponent equal to the number of factors. For 4 × 4 × 4 × 4, the result is 4^4.\"},{\"question\":\"What is the difference between GCF and LCM when working with factors?\",\"answer\":\"The GCF is the greatest number that divides both integers, while the LCM is the least common multiple shared by both. For example, GCF(42, 56) is 14 and LCM(8, 12) is 24.\"},{\"question\":\"How can you estimate square roots like √50 or √75 to the nearest whole number?\",\"answer\":\"Compare the value to nearby perfect squares. √50 is closest to 49 (7), and √75 is closest to 81 (9), so the nearest whole-number approximations are 7 and 9 respectively.\"}]","Exponents, Factors & Roots - Mixed Review (A) | PDF",1790135998]