express in simplest factored form (-1/2)x^-3/2 - (3/2 x)^-5/2?

Question

i don't know how to start, do i factor out the - (3/2 x)^-5/2 because its the lowest exponent?

it is read negative one half x to the power of negative three halves minus three halves x to the power negative five halves.

Answer 1

I am going to play a hunch and say that question should read : -

(-1/2) x^(-3/2) - (3/2) x^(-5/2)

= (-1/2) x^(-5/2) [x + 3]

Answer 2

Try this:

[-1 / (2x sqrt(x))] - [3 / (2x^2 sqrt(x))]

this is the same as:

[-x / (2x^2 sqrt(x))] - [3 / (2x^2 sqrt(x))]

which then becomes

(-x - 3) / (2x^2 sqrt(x))

this you can writ back to something similar to the starting form;
[-x - 3] (1/2) x^-5/2

which is indeed what como wrote;
[-x - 3] (1/2)x^-5/2 = (-1/2) [x + 3] x^-5/2