Question

If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]

Options

• 3

• 9

• 27

• 81

Answer 1

We have to find `3^(2(n/4-4))`

Given  `sqrt(2^n) = 1024`

`(sqrt(2^n) = 2^10`

`2^(nxx1/2) = 2^10`

Equating powers of rational exponents we get 

`n xx 1/2 = 10`

`n = 10 xx 2`

`n =20`

Substituting in  `3^(2(n/4-4))`   ``we get 

 `3^(2(n/4-4)) =  3^(2(20/4-4))`

`= 3^(2(5-4))`

` =3^(2xx1)`

`= 9`