開學了我上到中三得一條整數指數定律的數學題唔知點計出來幫幫下啦

👨🏻‍🏫 學術台數學

用戶24027

2007-09-14 4:24 am

開學了我上到中三得一條整數指數定律的數學題唔知點計出來幫幫下啦

1） 2的n次方+1次方除 8的n次方

答安是 1/2的2n次方-1

唔識怎麼計出來的幫幫我 THX~

回答 (4)

momo

2007-09-14 4:36 am

✔ 最佳答案

2^(n+1) / 8^n
= 2^(n+1) / 2^(3n)
= 2^(n+1) * 2^(-3n)
= 2^(n+1 -3n)
=2^(1-2n)
= (2^-(2n-1))
=(1/2)^(2n-1)

參考: My Calculation

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kimching

2007-09-24 4:52 am

2^(n+1) / 8^n

= 2^(n+1) / 2^(3n)

= 1/2^-(n+1) * 2^(3n)

= 1/2^(-n-1+3n)

=1/2^(2n-1)

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Timothy

2007-09-14 4:37 am

8的n次方 = (2的3次方)的n次方=2的3n次方

2的(n+1)次方除 8的n次方= 2的(n+1)次方除 2的3n次方
= 2的(n+1-3n)次方
= 2的(-2n+1)次方
= 2的(-1)(2n-1)次方
= 1/2 的(2n-1)次方

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doris

2007-09-14 4:36 am

(2^n+1)/8^n
= (2^n+1)/(2^3)^n
= (2^n+1)/(2^3n)
= 2^(n+1-3n)
= 2(-2n+1)
= 1/2^(2n-1)

參考: me

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