數學問題..

√a√a√a√a
= √a√a√a (a ^ 1/2)
= √a√a√a ^3/2
= √a√a [a ^ (3/2 x 1/2)]
= √a√a (a^3/4)
= √a√a ^ (1 + 3/4)
= √a√a ^(7/4)
= √a x [a^(7/4 x 1/2)
= √a x a ^ 7/8
= √a ^ (1+ 7/8)
= √a ^ (15/8)
= a ^ (15/8 x 1/2)
= a ^ (15/16)

我們可以續層拆, 方便打字, 我用sqrt(a) 代表 √a, 要知道 √a = a^(1/2)
sqrt( sqrt( sqrt( sqrt(a) ) ) )
= sqrt ( sqrt( sqrt ( a^(1/2) ) ) )
= sqrt ( sqrt ( (a^(1/2))^(1/2) ) )
= sqrt ( [ (a^(1/2))^(1/2) ]^(1/2) )
= [ [ (a^(1/2))^(1/2) ]^(1/2) ]^(1/2)
= a^[(1/2) * (1/2) * (1/2) * (1/2)]
= a^(1/(2^4))
= a^(1/16)

2007-08-02 23:01:49 補充：
x^y 係代表 x 的y 次方, x, y 係實數

2007-08-02 23:21:23 補充：
看錯題, 答案應是sqrt(a * sqrt(a * sqrt(a * sqrt(a) ) ) )= sqrt (a * sqrt(a * sqrt (a * a^(1/2) ) ) )= sqrt (a * sqrt (a * (a^(3/2))^(1/2) ) )= sqrt (a * sqrt (a * (a^(3/4)) )= sqrt (a * sqrt (a^7/4))= sqrt (a * (a^(7/4))^(1/2) )= sqrt (a * a^(7/8))= (a^15/8)^(1/2)= a^(15/16)