How to simplify $x^{1/2}$

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I study the roots laws and this is one of them:

$$\sqrt x = x^{1/2}$$

I don't know how simplify the $x^{1/2}$, what I mean is...

If for example:

$$x^{-3}=1 \cdot 1/x \cdot 1/x \cdot 1/x = 1/x^3$$

How do I simplify:

$$x^{1/2} = ?$$

Edit:

This edit is written to explain the meaning of simplify:

We all know that $3^3=1*3*3*3 = 27$

The 1*3*3*3 above is a simplification for $3^3$, in my question I ask if there is a way to simplify $x^{1/2}$

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3 Answers

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There is no easy way to simplify $x^{\frac12}$, except by writing it as $x^{\frac12}=\sqrt x$

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Reading between the lines are you trying to justify the result?

Consider:

$x^a \times x^a= x^1$

Using power laws you get $x^{2a}=x^1$

Comparing powers $a=\frac{1}{2}$

...but $\sqrt{x}\times \sqrt{x}=x$

so to preserve the power laws $x^{1/2}=\sqrt{x}$.

I think this is as simple as the identity gets but I like the expression by @logicmonkey for $x\neq0$

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You might occasionally want to write it as $\frac {{x}}{{\sqrt x}}$

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