Help simplify a simple algebraic equation x^{1/2}/x^2

As you see in the title, I'm wondering if there's anything I can do to simplify the equation.
Here is a link for a proper representation
http://texify.com/?$\frac{x^{1/2}}{x^2}$

By simplify, I mean that this
http://texify.com/?$\frac{x^{3}y^{3}}{x^4y{1}}$
can be turned into this
http://texify.com/?$\frac{y^{2}}{x}$

Help me please :D

x^(1/2) / x^2

law of exponents; divide the bases, subtract the exponents

x^(1/2 - 2)

x^(1/2 - 4/2)

x^(-3/2)

law of exponents; to the power of a negative, flip fraction and make power positive

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

(1/x) ^ (3/2)

1/x^(3/2)

that would be simplified exponent form, but you could always put this in simplified radical form, in which case keep going.

1/√(x)^3

1/√x^3

but simplify

1/(√x^2 times √x)

1/(x^(2/2) times √x)

1/(x^1 times √x)

1/(x√x)

and now rationalize by multiplying top and bottom by the denominator

1(x√x) / x√x(x√x)

x√x / x^2√x^2

x√x / x^2[x^(2/2)]

x√x / x^2[x^1]

x√x / x^3

NOTE that x^1 goes into x^1 with nothing left over and into x^3 with x^2 left over

√x / x^2

cant' simplify further

Generally, x^a/x^b = x^(a - b)
x^(1/2)/x^2 =
x^((1/2) - 2) =
x^(-3/2) = 1/x^(3/2)

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

x^(1/2) / x^2
= x^(1/2 - 2)
= x^(-3/2)
= 1 / x^(3/2)
= 1 / sqrt(x^3)