The value of` ((log_(2)9)^(2))^(1/(log_(2)(log_(2)9)))xx(sqrt7)^(1/(log_(4)7))` is ________.

Answer

8

Explanation

`E = ((log_(2)9)^(2))^(1/(log_(2)(log_(2)9)))xx(sqrt7)^(1/(log_(4) 7))`
` ((log_(2)9)^(2))^(1/(log_(2)(log_(2)9)))=((log_(2)9)^(2))^(log_((log_(2)9)^(2)))`
` = (log_(2)9)^(2log_((log_(2)9)^(2)))`
` = (log_(2)9)^(log_((log_(2)9)^(4)))=4`
` (sqrt7)^(1/(log_(4)7))=(7)^(1/2log_(7)4)=7^(log_(7)2)=2`
` :. E=4xx2 = 8`