Re: [計算] 指數律小哉問
: 推 iambahamut:以2^3^2為例 依照上面算法會是2^9=512 08/03 21:39
http://lmgtfy.com/?q=2%5E3%5E2 (誤)
: → iambahamut:實際是2^3=8 8^2 =64 = 2^6 08/03 21:40
: → iambahamut:指數算法其實直接相乘就好原式=(5^4)^(2x3)=5^4^6 08/03 21:41
: → iambahamut:5^4^6=5^24 答案就是5的24次方 08/03 21:41
: 推 iambahamut:除非原意是5^[4^(3^2)]才會是上面這個答案 08/03 21:44
一般情況而言 ,只有(a^m)^n =a^mn ,而沒有 a^m^n=a^mn
a^m^n讀法是
"a的 m^n次方" (要計算結果則先計算 m^n)
而不是
"a^m的n次方" (要計算結果則先算 a^m )
http://en.wikipedia.org/wiki/Exponentiation
看這段 :
[edit]
Identities and properties
.
.
.
Similarly, while addition and multiplication are associative (for example,
(2+3)+4 = 9 = 2+(3+4) and (2·3)·4 = 24 = 2·(3·4), exponentiation is not
associative either: 23 to the 4th power is 84 or 4096, but 2 to the 34 power
is 281 or 2,417,851,639,229,258,349,412,352. Without parentheses to modify
the order of calculation, the order is usually understood to be top-down, not
bottom-up:
以上淺見 ,有錯請指正 ^^/
ps....如果要說wiki的資料不見得正確的話 ,煩請各位幫忙找更有說服力的教材><;;
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