IGCSE›Cambridge IGCSE Maths›Mind mapsAlgebraic Roots & IndicesCambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsIndex lawsMultiply: am×an=am+na^m \times a^n = a^{m+n}am×an=am+nDivide: am÷an=am−na^m \div a^n = a^{m-n}am÷an=am−nPower of a power: (am)n=amn(a^m)^n = a^{mn}(am)n=amn(5x3)2=25x6(5x^3)^2 = 25x^6(5x3)2=25x6Special indicesZero index: a0=1a^0 = \mathbf{1}a0=1Negative index means reciprocal: a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1Fractional: a1n=ana^{\frac{1}{n}} = \sqrt[n]{a}an1=naamn=(an)ma^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^manm=(na)m1614=216^{\frac{1}{4}} = \mathbf{2}1641=2Indicespowers and rootsama^mama0a^0a0a−na^{-n}a−nSimplifying Multiply or divide the coefficients Add indices to multiply, subtract to divide Combine into one term 12a5÷3a−2=4a712a^5 \div 3a^{-2} = 4a^712a5÷3a−2=4a7SolvingWrite both sides with the same baseThen equate the indices2x=32=252^x = 32 = 2^52x=32=25, so x=5x = 5x=55x+1=52x5^{x+1} = 5^{2x}5x+1=52x gives x=1x = 1x=1Exam tipsNegative index does not make a negative valueShow coefficient and index working separatelyNo logarithms needed