Question

If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =

Options

• \[\frac{\sqrt{2}}{4}\]

• \[\sqrt[2]{2}\]

• 4

• 64

Answer 1

For `x /(x^1.5) = 8x^-1`, we have to find the value of x.

So,

`x^1 /(x^1.5) = 8x^-1`

`x ^(1-1.5) = 8x^-1`

`x ^(-0.5) = 2^3x^-1`

`(x^0.5) /x^-1= 2^3`

`x^(-5/10) /x^-1= 2^3`

`x^(-1/2+1)= 2^3`

`x^(-1/2+2/2)= 2^3`

`x^((-1+2)/2) = 2^3`

`x^(1/2) = 2^3`

By raising both sides to the power 2 we get

`x^(1/2xx2) = 2 ^(3xx2)`

`x^(1/2xx2) = 2 ^6`

`x^1 = 64`

The value of  x is 64.