[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267369-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-267369-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-and-radicals-algebra-practice-worksheet","Exponents and Radicals - Algebra practice worksheet","","Practice set focused on simplifying expressions involving exponents and radicals, including evaluating powers, applying rules for multiplying like bases, and handling negative exponents by rewriting them as reciprocals. Tasks progress from evaluating given expressions to simplifying products and quotients, eliminating negative powers, and expressing results in the form x^r. The worksheet includes sections for evaluating using provided variable values and an answer key.",{"@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-and-radicals-algebra-practice-worksheet/267369/",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-and-radicals-algebra-practice-worksheet/267369.png","ImageObject",300,407,{"name":42,"@type":43},"Mary Man","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",16,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you simplify radical or exponent expressions in this worksheet?","Question",{"text":63,"@type":64},"Use prime factorization and power-canceling rules, then rewrite results to remove negative exponents when required.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What does “eliminate negative exponents” mean here?",{"text":68,"@type":64},"Rewrite any term with a negative exponent as its reciprocal with a positive exponent, then simplify the resulting expression.",{"name":70,"@type":61,"acceptedAnswer":71},"How are answers found for problems that say “use the values given”?",{"text":72,"@type":64},"Substitute the provided values for each variable, then evaluate the expression step by step using standard order of operations.","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},267369,1789417817,{"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":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":106,"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":80,"read_time":144},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Tip. When simplifying radical expressions, it is helpful to rewrite a number using its prime factorization and cancel powers.  \nExample. 108 = 2233 so p3108 = 3p2233 = 3 3p22 = 3 p34  \n1. Evaluate each expression.  \n(a) (−3)4 (b) −34 (c) ✓ 18◆2 · (−2)3  \n(d) (−2)5 (e) −25 (f) (−6)2 · ✓16◆2  \n(g) ✓ ~~ ~~25◆0 · 3−1 (h) 352~~ ~~ (i) ✓ ~~ ~~2 ◆−2  \n(j) 52 · 5 (k) 58 · 5−6 (l) 5−8 · 56  \n(m) \\#23 $2 (n) 108105~~ ~~ (o) 11002  \n2. Simplify.  \n(a) p 12 (b) p 18 (c) p3250  \n(d) p5243 (e) p5486 (f) p4162  \n(g) r ~~ ~~2716  (h) p~~ ~~18p~~ ~~36 (i) 5 p381  \n(j) p2 · p6 (k) p 14 · p32 (l) p~~ ~~80p~~ ~~5  \n(m) p3500 (n) p424 · p414 (o) p~~ ~~63p~~ ~~7  \n(p) r5 12 · r5 116  \n3. Simplify each expression and eliminate negative exponents.  \n(a) x5 · x8 (b) (2x3 )2 (c) x−3 · x5  \n(d) y 6 · y 9 (e) (3x)3 (f) y 7 · y −3  \n(g) z −8 · z 3 (h) x−2x−6x4 (i) xx1150  \n(j) y 3 · y −9 (k) w 5 w −8w4 (l) x8~~ ~~xx120  \n(m) b8~~ ~~bb−3~~ ~~ (n) (z3 z 5 )2 (o) (3x4 ) ⇣ x3⌘3  \n(p) yy23~~ ~~yy3~~ ~~ (q) (−2b3 b3 )3 (r) (−3x2 )2 (2x−2)3  \n4. Simplify each expression and eliminate negative exponents.  \n(a) 7x−2~~ ~~ (b) 47y6y5~~ ~~z4~~ ~~ (c) (x3 y −5)(2x−4y 2 )(4xy 5 )  \n(d) (xw)(6x−6w −4) (e) (w · 4w2 · w2 )3 (f) ✓ y2y◆3  \n(g) (3x · 4x2 )3 (h) ✓ ~~ ~~2y44y ◆2 (i) ✓ 9z8z6 ◆3  \n(j) x−3y−2~~ ~~ (k) ✓ aab3−b22 ◆3 (l) ✓ xy2 ◆5 ✓ x2~~ ~~yz23 ◆3  \n(m) ((a−a21b33))23~~ ~~ (n) ✓ x2~~ ~~z2y54 ◆✓ 3x2z2y~~ ~~3 ◆2 (o) (w(w22~~ ~~v)33)2  \n(p) 16x4xy−6~~ ~~y85~~ ~~ (q) ⇣ 33 ⌘−2 (r) ✓ 2x−1y ◆−3  \n5. Express the following in the form xr .  \n(a) ( p5x)6 (b) 8px3  (c) (~~ ~~1~~x~~p)5~~ ~~ (d) 1p3~~ ~~x4~~ ~~ (e) q4 p3x (f) s ~~ ~~x  \n6. Express the following in the form xr .  \n(a) x ~~5~~2 x3   (b) xx674~~ ~~ (c) (x3 ) − ~~4~~5 (d) x ~~7~~5 x − ~~8~~3 (e) (x~~2~~3 ) ~~4~~9 (f) x1~~5~~2  \n(g) ✓ 1x3 ◆ − 23 (h) x~~ ~~1px (i) x2 ( p3x) (j) xx~~2~~5~~ ~~ (k) xx13~~ ~~ (l) x~~5~~4  \n7. Simplify and eliminate negative exponents. Assume that all letters denote positive numbers.  \n(a) x ~~2~~3 · x ~~4~~3  \n(d) ((2b)~~2~~9 )3 · (2b)  \n(g) (x5 y4 ) − ~~1~~2  \n1 3  \n(b)  \n(e)  \n(h)  \na ~~3~~5 · a ~~ 1~~5~~2 ~~x ~~3~~2 x ~~1~~2 x ~~5~~2  \n(−8x6 y −18) − ~~1~~3  \n(c) (9x)~~1~~2 · (4x~~1~~4 )  \n(f) (27z3 ) − ~~2~~3 y −1(yx ~~1~~2 ) ~~2~~3  \n(i) ~~ ~~3212~~ ~~ !4 ✓ ab−32 ◆ (j) ✓ x26~~ ~~y7y3 ◆ − 13  \nAnswers  \n1. (a) 81 (b) −81 (c) −1/8 (d) −32 (e) −32 (f) 1 (g) 1/3 (h) 1/9  \n(i) 25/4 (j) 125 (k) 25 (l) 1/25 (m) 64 (n) 1000 (o) 10,000  \n2. (a) 2 p3 (b) 3 p2 (c) 5 p32 (d) 3 (e) 3 p52 (f) 3 p42 (g) 3~~ ~~p43 (h)  ~~ ~~p22  \n ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ 1  \n(i) 15 p33 (j) 2 p3 (k) 8 p7 (l) 4 (m) 5 p34 (n) 2 p421 (o) 3 (p)  \n2  \n3. (a) x 13 (b) 4x6 (c) x2 (d) y 15 (e) 27x3 (f) y4 (g) 1z5~~ ~~ (h) 1x4~~ ~~ (i) x5 (j) 1y6~~ ~~ (k) w (l) 1x4~~ ~~ (m) b4 (n) z 16 (o) x79~~ ~~ (p) y 9 (q) −8b18 (r) 7x22  \n4. (a) x5~~ ~~y73~~ ~~ (b) 7y4z4~~ ~~ (c) 8y 2 (d) x56w3~~ ~~ (e) 64w15 (f) y 3 (g) 1728x9 (h) y64 (i) 571229z15~~ ~~ (j) x13y~~ ~~ (k) a18b12~~ ~~ (l) x11yz6~~ ~~ (m) b1a58~~ ~~ (n) 9x62y~~ ~~ (o) w 2 v 9 (p) 4xy193 (q) w~~ ~~92x6~~ ~~ (r) 8x16y~~ ~~9  \n6  3 − 5 − 4  1   1   \n5. (a) x 5 (b) x 8 (c) x 2 (d) x 3 (e) x 12 (f) x − 10  \nID: 1  \nKeystone Algebra 1 Name___________________________________  \nSimplifying Absolute Value Problems Date________________ Period____  \n© 2 0 1 2 Kouta SofBt ware LBL0C . Avll rights reserved.  \nEvaluate each expression.  \n1)  −1 − 2  2) 9 ÷ (  3  )  \n3)  1 − 4  × −2  12   \n4) −  \n−1  + 1  \n5)  1 − −3  +  5  6) (  3 − 3  − −4) × 5  \nEvaluate each using the values given.  \n7) b −  a  ; use a = 5, and b = 6 8)  x + y  ; use x = 3, and y = −5  \n9) q −  r  ; use q = 3, and r = −1 10)  j − h  ; use h = 5, and j = 6  \n© 2 01 2 Kiuta So fTt ware LL C . AblLlO rifghDt s res erved . MaEde w iCt hv Infki1nZiwt e Pre-A4l3geb ra. -1-  \n11) x − (  z  + x); use x = 6, and z = 3 12) 6  x + y  ; use x = 1, and y = 1  \n13) (  p + q  ) ÷ 5; use p = −2, and q = −3 14) j (h −  h  ); use h = −1, and j = 5  \n15)  2  + h +  j  ; use h = 6, and j = −4 16)  x − y  + y − 1; use x = −3, and y","cbCaicnjIZvQc6Pv","https://ap.wps.com/l/cbCaicnjIZvQc6Pv","pdf",231988,"English","# Evaluate each expression\n## Simplify\n# Eliminate negative exponents\n## Express in the form x^r\n# Evaluate using given values\n## Absolute value and variable substitution","[{\"question\":\"How do you simplify radical or exponent expressions in this worksheet?\",\"answer\":\"Use prime factorization and power-canceling rules, then rewrite results to remove negative exponents when required.\"},{\"question\":\"What does “eliminate negative exponents” mean here?\",\"answer\":\"Rewrite any term with a negative exponent as its reciprocal with a positive exponent, then simplify the resulting expression.\"},{\"question\":\"How are answers found for problems that say “use the values given”?\",\"answer\":\"Substitute the provided values for each variable, then evaluate the expression step by step using standard order of operations.\"}]","Exponents and Radicals - Algebra practice worksheet | PDF",18]