- Choice D
Rule name Rule Example Product rules *a*⋅^{ n}*a*=^{ m}*a*^{ n+m}2 ^{3}⋅ 2^{4}= 2^{3+4}= 128*a*⋅^{ n}*b*= (^{ n}*a*⋅*b*)^{ n}3 ^{2}⋅ 4^{2}= (3⋅4)^{2}= 144Quotient rules *a*/^{ n}*a*=^{ m}*a*^{ n}^{–m}2 ^{5}/ 2^{3}= 2^{5-3}= 4*a*/^{ n}*b*= (^{ n}*a*/*b*)^{ n}4 ^{3}/ 2^{3}= (4/2)^{3}= 8Power rules ( *b*)^{n}^{m}=*b*^{n⋅m}(2 ^{3})^{2}= 2^{3⋅2}= 64_{b}n^{m}_{= b}(*n*^{m})_{2}3^{2}_{= 2}(3^{2})_{= 512}^{m}√(*b*) =^{n}*b*^{n/m}^{2}√(2^{6}) = 2^{6/2}= 8*b*^{1/n}=√^{n}*b*8 ^{1/3}=^{3}√8 = 2Negative exponents *b*= 1 /^{-n}*b*^{n}2 ^{-3}= 1/2^{3}= 0.125Zero rules *b*^{0}= 15 ^{0}= 10 = 0 , for^{n}*n*>00 ^{5}= 0One rules *b*^{1}=*b*5 ^{1}= 51 = 1^{n}1 ^{5}= 1Minus one rule (-1) ^{n}= -1 , n odd v

(-1)^{n}= 1 , n even(-1) ^{5}= -1Derivative rule ( *x*)^{n}*‘*=*n*⋅*x*^{ n}^{-1}( *x*^{3})*‘*= 3⋅*x*^{3-1}Integral rule ∫ *x*=^{n}dx*x*^{n}^{+1}/(*n*+1)+*C*∫ *x*^{2}*dx*=*x*^{2+1}/(2+1)+*C*4b8⋅5b3 = 4⋅5⋅b8+3=20b11

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