Question

If x^ (3/ 2) = 64, find the value of (4x)^−3 /4.

Answer 1

The answer will be
`(1)/(256)`

Explanation:

We have given that
`x^{(3)/(2)}=64`

And we have to find the value of
`(4x)^{(-4)/(3)}`

As
`x^{(3)/(2)}=64`

`x=(64)^{(2)/(3)}=(4^3)^(2)/(3)=4^2=16`

So the value of x = 16

Now we have to find the value of
`(4x)^{(-4)/(3)}`

So
`(4* 16)^{(-4)/(3)}=(64)^{(-4)/(3)}=(4^3)^{(-4)/(3)}=4^(-4)=(1)/(4^4)=(1)/(256)`