IGCSE›Edexcel IGCSE Maths›Mind mapsAlgebra ToolkitEdexcel IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsIndex notationana^nan: base multiplied by itself n timesa1=aa^1=aa1=aa0=a^0=a0= 1 for any non-zero aa−n=1ana^{-n}=\frac{1}{a^n}a−n=an1a1n=ana^{\frac{1}{n}}=\sqrt[n]{a}an1=naIndex lawsSame base onlyMultiply: add indices, am×an=am+na^m\times a^n=a^{m+n}am×an=am+nDivide: subtract indicesPower of a power: multiply indices, (am)n=amn(a^m)^n=a^{mn}(am)n=amn823=22=48^{\frac{2}{3}}=2^2=4832=22=4Algebra Toolkitindices and termsana^nana0a^0a0a−na^{-n}a−nSubstitutionReplace letters with values in bracketsThen apply BIDMAS2x2−3y2x^2-3y2x2−3y at x=−3,y=4x=-3,y=4x=−3,y=4: 2(9)−12=62(9)-12=62(9)−12=6(−3)2=(-3)^2=(−3)2= 9, not −9-9−9Like termsSame letters and same powersAdd or subtract the coefficients3x+5x=8x3x+5x=8x3x+5x=8x3x3x3x and 5x25x^25x2 are not like terms4x2+3x−2x2+7−5x=2x2−2x+74x^2+3x-2x^2+7-5x=2x^2-2x+74x2+3x−2x2+7−5x=2x2−2x+7Exam tipsSay it aloud: same base, multiplying, so addx3×x2=x5x^3\times x^2=x^5x3×x2=x5, not x6x^6x6Colour-code matching terms in long expressions