[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571808-105":53,"doc-detail-571808-en":126},{"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":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","my-laws-of-exponents-cheat-sheet-algebra-cheat-sheet-basic-properties-facts","My “Laws of Exponents” Cheat Sheet - Algebra Cheat Sheet Basic Properties & Facts","","My “Laws of Exponents” cheat sheet summarizes key exponent rules for multiplying and dividing powers with the same base, power of a power, negative exponents, and the zero exponent rule. It also compiles essential algebra fundamentals including arithmetic identities, properties of inequalities and absolute value, distance formula, and complex number operations. Additional sections cover logarithm definitions and properties, factoring and quadratic solving formulas, completing the square, and core function and graph types such as linear, slope-intercept forms, parabolas, circles, ellipses, and hyperbolas.",{"@graph":63,"@context":118},[64,80,101],{"@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":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/my-laws-of-exponents-cheat-sheet-algebra-cheat-sheet-basic-properties-facts/571808/",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/my-laws-of-exponents-cheat-sheet-algebra-cheat-sheet-basic-properties-facts/571808.png","ImageObject",442,249,{"name":88,"@type":89},"A glass of water","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the rules for multiplying and dividing powers with the same base?","Question",{"text":108,"@type":109},"For the same base, multiplying powers adds exponents (xa · xb = xa+b). Dividing powers subtracts exponents (xa / xb = xa-b, shown as xa - b).","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do negative exponents and zero exponents work?",{"text":113,"@type":109},"A negative exponent rewrites as a reciprocal power (x-a = 1/xa, illustrated with x-7 = 1/x7 in the sheet). Any nonzero base to the power of zero equals 1 (x0 = 1; example given with 50 = 1).",{"name":115,"@type":106,"acceptedAnswer":116},"Which key formulas are included for solving algebra problems like quadratics and functions?",{"text":117,"@type":109},"The sheet includes the quadratic formula for ax^2 + bx + c = 0 and steps for completing the square. It also lists function forms such as y = mx + b and parabola forms like y = a(x-h)^2 + k, plus basic graph descriptions for circles, ellipses, and hyperbolas.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571808,1792055144,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"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":141},962090760832,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","NAME \nMy “Laws of Exponents” Cheat Sheet \n􀀁 Multiplying Powers with the Same Base General Rule: xa ● xb = xa+b Example: x5 ● x6 = x 11 \n􀀁 Dividing Powers with the Same Base General Rule: ~~ ~~xxab~~ ~~ = xa – b Example: ~~ ~~xx74 = x3 \n􀀁 Finding a Power of a Power General Rule: (xa)b = xa ●b Example: (x3)6 = x 18 \n􀀁 Negative Exponents General Rule: x-a = ~~ ~~x1a Example: x-7 = ~~ ~~x17 \n􀀁 Zero as an Exponent General Rule: x0 = 1 Example: 50 = 1 \nNAME \nMy “Laws of Exponents” Cheat Sheet \n􀀁 Multiplying Powers with the Same Base General Rule: xa ● xb = xa+b Example: x5 ● x6 = x 11 \n􀀁 Dividing Powers with the Same Base General Rule: ~~ ~~xxab~~ ~~ = xa – b Example: ~~ ~~xx74 = x3 \n􀀁 Finding a Power of a Power General Rule: (xa)b = xa ●b Example: (x3)6 = x 18 \n􀀁 Negative Exponents General Rule: x-a = ~~ ~~x1a Example: x-7 = ~~ ~~x17 \n􀀁 Zero as an Exponent General Rule: x0 = 1 Example: 50 = 1 \nAlgebra Cheat Sheet Basic Properties & Facts \nArithmetic Operations \nab + ac = a (b + c) \nÊÁË ~~ ~~ab~~ ~~ ˆ¯˜ = a c bc \na c ad + bc ~~ ~~ + ~~ ~~ = ~~ ~~b d bd \na-b b-a ~~ ~~ = ~~ ~~c-d d-c \nab~~ ~~+a~~ ~~ac = b + c, a 􀂹 0 \nExponent Properties \nn m n+m \na a = a \nProperties of Inequalities \nIf a \u003C b then a + c \u003C b + c and a-c \u003C b-c If a \u003C b and c > 0 then ac \u003C bc and a \u003C bc c \nIf a \u003C b and c \u003C 0 then ac > bc and a > bc c \nProperties of Absolute Value \nÏa \na = ÌÓ-a \na 􀂳 0 \nab = ab \nifa 􀂳 0 \nif a \u003C 0 \na + b £ a + b Triangle Inequality \nDistance Formula \nIf P1 = ( x1, y1 ) and P2 = ( x2 , y2 ) are two points the distance between them is \n( )m \nn nm \na = a \na0 = 1, a 􀂹 0 d (P1 , P2 ) = \n( x2-x1 )2 + (y2-y1 )2 \nComplex Numbers \ni = -1 i2 = -1 -a = i, a 􀂳 0 \n( a + bi) + ( c + di) = a + c + ( b + d) i \n( a + bi)- (c + di) = a-c + ( b-d) i ( a + bi)( c + di) = ac-bd + (ad + bc) i ( a + bi)( a-bi) = a2 + b2 \na + bi = a2 + b2 Complex Modulus \n( a + bi) = a-bi Complex Conjugate \n( a + bi) ( a + bi) = a + bi2 \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). © 2005 Paul Dawkins \nLogarithms and Log Properties \nDefinition \ny = logb x is equivalent to x = by \nExample \nlog5 125 = 3 because 53 = 125 \nSpecial Logarithms \nln x = log e x natural log log x = log10 x common log where e = 2.718281828K \nLogarithm Properties logb b = 1 logb 1 = 0 logb bx = x blog b x = x logb ( x r) = r logb x \nlogb ( xy) = logb x + logb y logb ÊÁ ~~ ~~x~~ ~~ ˆ˜ = logb x-logb y \nË y ¯ \nThe domain of logb x is x > 0 \nFactoring and Solving \nFactoring Formulas \nx2-a2 = ( x + a) ( x-a ) x2 + 2ax + a2 = ( x + a)2 \nx2-2ax + a2 = ( x-a)2 \nx2 + (a + b) x + ab = (x + a)( x + b) x3 + 3ax2 + 3a2x + a3 = ( x + a )3 \nx3-3ax2 + 3a2x-a3 = ( x-a )3 x3 + a3 = ( x + a) ( x2-ax + a2 ) \nx3-a3 = ( x-a) ( x2 + ax + a2 ) x2n-a2n = ( xn-an)( xn + an) If n is odd then, \nxn-an = ( x-a) ( xn-1 + ax n-2 +L + an-1 ) n n \nx + a \n= ( x + a) ( xn-1-axn-2 + a2xn-3-L + an-1 ) \nQuadratic Formula \nSolve ax2 + bx + c = 0 , a 􀂹 0 \n-b ± b2-4ac x = ~~ ~~ \n2a \nIf b2-4ac > 0 -Two real unequal solns. If b2-4ac = 0 -Repeated real solution. If b2-4ac \u003C 0 -Two complex solutions. \nSquare Root Property \nIf x2 = p then x = ± \nAbsolute Value Equations/Inequalities \nIf b is a positive number \np = b \np \u003C b \np > b \nfi \nfi \nfi \np = -b or-b \u003C p \u003C bp \u003C -b or \np = b \np > b \nCompleting the Square \nSolve 2x2-6x-10 = 0 \n( 1) Divide by the coefficient of the x2 x2-3x-5 = 0 \n(2) Move the constant to the other side. x2-3x = 5 \n(3) Take half the coefficient of x, square it and add it to both sides \nx2-3x + ÁÊË - ~~ ~~32ˆ¯˜2 = 5 + ÁÊË - ~~ ~~32ˆ¯˜2 = 5 + ~~ ~~94 = ~~ ~~294 \n(4) Factor the left side \nÊ ~~ ~~3~~ ~~ ˆ˜2 ~~ ~~29 \nÁËx-2 ¯ = 4 \n(5) Use Square Root Property \n3 29 29 x- ~~ ~~ = ± ~~ ~~ = ± ~~ ~~ \n2 4 2 \n(6) Solve for x \n3 29 x = ± ~~ ~~ \n2 2 \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). ","cbCaihP8gSdUyFO3","https://ap.wps.com/l/cbCaihP8gSdUyFO3","pdf",1026545,20,"English","# My “Laws of Exponents” Cheat Sheet\n## Algebra Cheat Sheet Basic Properties & Facts\n# Arithmetic Operations\n# Exponent Properties\n# Properties of Inequalities\n# Properties of Absolute Value\n# Distance Formula\n# Complex Numbers\n# Logarithms and Log Properties\n# Factoring and Solving\n# Quadratic Formula\n# Completing the Square\n# Functions and Graphs\n## Constant Function\n## Line/Linear Function\n## Parabola/Quadratic Function\n## Circle\n## Ellipse\n## Hyperbola","[{\"question\":\"What are the rules for multiplying and dividing powers with the same base?\",\"answer\":\"For the same base, multiplying powers adds exponents (xa · xb = xa+b). Dividing powers subtracts exponents (xa / xb = xa-b, shown as xa - b).\"},{\"question\":\"How do negative exponents and zero exponents work?\",\"answer\":\"A negative exponent rewrites as a reciprocal power (x-a = 1/xa, illustrated with x-7 = 1/x7 in the sheet). Any nonzero base to the power of zero equals 1 (x0 = 1; example given with 50 = 1).\"},{\"question\":\"Which key formulas are included for solving algebra problems like quadratics and functions?\",\"answer\":\"The sheet includes the quadratic formula for ax^2 + bx + c = 0 and steps for completing the square. It also lists function forms such as y = mx + b and parabola forms like y = a(x-h)^2 + k, plus basic graph descriptions for circles, ellipses, and hyperbolas.\"}]","My “Laws of Exponents” Cheat Sheet - Algebra Cheat Sheet Basic Properties & Facts | PDF",1791923792,7]