標題:
exponential equatio question2
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(^3√-2)^3 ^3√(-2)^3 ^4√(-2)^4 (-^3√3)^9 ^5√√-2^20 √63√-2^6 √^3√729 ^3√√64 √75/√3 ^3√2/^3√54 ^4√6/^4/√96 √^3√8 √^3√16 更新: ^4√6/^4√96 問題有冇打錯?? 更新 2: √^3√2^6 √8x√2 ^3√2x^3√4 ^3√12x^3√18 ^3√2^5x^3√16 ^3√2^5x^3√16 ^4√400/√10 ^3√2/^3√16 ^3√2/^3√-16
最佳解答:
(^3√-2)^3 = -2^(1/3 x 3) = -2^1 = -2 ^3√(-2)^3 = ^3√-8 = -2 ^4√(-2)^4 = ^4√16 = 2 or -2 (-^3√3)^9 = 3^(-1/3 x 9) = 3^-3 = 1/27 ^5√√-2^20 =^5√( -2^(20/2) ) = ^5√(-2^10) = -2^(10/5) = -2^2 = 4 √63√-2^6 = (√63) x (√64) = (√63) x 8 = 8 x 3√7 = 24√7 √^3√729 = √^3√(9x9x9) = √9 = 3 or -3 ^3√√64 = ^3√8 or = ^3√-8 = ^3√(2x2x2) or = ^3√(-2x-2x-2) = 2 or -2 √75/√3 = √(75/3) = √25 = 5 or -5 ^3√2/^3√54 = ^3√( 2 / 3√2 ) = ^3√( √2 / 3 ) = ^6√2 / ^3√3 or (-)^6√2 / ^3√3 ^4√6/^4/√96 問題有冇打錯?? √^3√8 = √^3√(2x2x2) = √2 or -√2 √^3√16 = ^3√( √16 ) = ^3√4 = ^3√4 or ^3√(-4) 有唔明白, 請問~!!??!! 2009-02-02 17:11:34 補充： 2009-02-02 17:01:26 補充 ^4√6/^4√96 = ^4√( 6 / 2√6 ) = ^4√( √6 / 2 ) = ^4√( 6^(1/2) / 2 ) = 6^(1/2 x 1/4) / 2^(1/4) = 6^(1/8) / 2^(1/4) = ^8√6 / ^4√2 or (-)^8√6 / ^4√2 2009-02-02 17:50:39 補充： √^3√2^6 = ^6√( 2^6 ) = 2 or -2 √8x√2 = √16 = 2 or -2 ^3√2x^3√4 = ^3√( 2x4 ) = ^3√8 = 2 2009-02-02 17:50:59 補充： ^3√12x^3√18 = ^3√( 12x18 ) = ^3√216 = ^3√(6x6x6) = 6 ^3√2^5x^3√16 = ^3√( 2^5 x 16 ) = ^3√512 = ^3√(8x8x8) = 8 ^3√2^5x^3√-16 = ^3√( 2^5 x -16 ) = ^3√-512 = ^3√(-8x-8x-8) = -8 2009-02-02 17:51:36 補充： ^4√400/√10 = ^4√( 40√10 ) = ^4√( 40 x 10^(1/2) ) = 40^(1/4) x 10^(1/8) = ( ^4√40 )( ^8√10 ) or (-)( ^4√40 )( ^8√10 ) 2009-02-02 17:51:42 補充： ^3√2/^3√16 = ^3√( 2 x^3√16 x^3√16 / ^3√16 x^3√16 x^3√16 ) = ^3√( 2 x^3√(2^4)^2 / 16 ) = ^3√( (2^8/3) / 8 ) = ( (2^8/3) / 8 )^(1/3) = ( 2^( 8/3 ))^(1/3) / 8^(1/3) = 2^(8/9) / 2 = 2^(8/9 -1) = 2^-1/9 = 1/2^(1/9) ^3√2/^3√-16 jump steps from the above question... = 2^(8/9) / -2 = -2^(8/9 -1) = -2^-1/9 = -1/2^(1/9)
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