数字系统

练习1.6

指数的重要定律:

问题1:找到

(我)64年^ (1/2)

答:, 64年^ (1/2)

' = (8 xx8) ^ (1/2) = (8 ^ 2) ^ (1/2)

' = 8 ^ (2 xx1/2) = 8 ^ 1 = 8 '

(2)“32 ^(1/5)”

答:, ' 32 ^ (1/5)

' = (2 xx2xx2xx2xx2) ^ (1/5)

' = 2 ^ (5 xx1/5) = 2 ^ 1 = 2 '

(3)125年^ (1/3)

答:, 125年^ (1/3)

' = (5 xx5xx5) ^ (1/3)

' =(5 ^ 3) ^(1/3) = 5 ^ 1 = 5”

问题2:找到

(我)9 ^(3/2)”

答:,“9 ^ (3/2)'

' = (3 ^ 2) ^ (3/2) '

' = 3 ^ (2 xx3/2) = 3 ^ 3 = 27 '

(2)“32 ^(2/5)”

答:, ' 32 ^ (2/5)

' = (2 xx2xx2xx2xx2) ^ (2/5)

' = (2 ^ 5) ^ (2/5) = 2 ^ (5 xx2/5) = 2 ^ 2 = 4 '

(3)“16 ^ (3/4)

答:鉴于,16 ^ (3/4)

' = (2 xx2xx2xx2) ^ (3/4)

' = (2 ^ 4) ^ (3/4) = 2 ^ (4 xx3/4) = 2 ^ 3 = 8 '

(iv)125年^ (1/3)

答:, 125年^ (1/3)

' = (5 xx5xx5) ^ (1/3)

' = (5 ^ 3) ^ ^ (1/3) = 5 (3 xx-1/3) = 5 ^ 1 = 1/5 '

问题3:简化

(我)2 ^(2/3)。2 ^ (1/5)

答:, ' 2 ^(2/3)。2 ^ (1/5)

以后,“^硕士^ n = ^ (m + n) '

' = (2) ^ (2/3 + 1/5) = (2) ^ ((10 + 3) / 15) = 2 ^ (13/15)

(2)(1 /(3 ^ 3)) ^ 7”

答:,“(1 /(3 ^ 3))^ 7”

' = 7 = 3 (3 ^ 3) ^ ^ (3 xx7) = 3 ^ -21年

(3)(11 ^(1/2)) /(11 ^(1/4))”

答:,“(11 ^(1/2))/(11 ^(1/4))”

' = (11) ^ (1/2-1/4) = (11) ^ ((2 - 1) / 4) = 11 ^ 1/4 '

(iv)7 ^(1/2)。8 ^ (1/2)

答:,“7 ^(1/2)。8 ^ (1/2)

我们知道，a^m ^ b^m=(ab)^m

' = (7 xx8) ^ (1/2) = 56 ^ (1/2)