Can you take a fractional root of a number?

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Is it possible to say, take a 1,5th root of 2? And if not why so? Wouldn’t a 0,5th root of a to the third power = a to the power of 3/0,5 = a to the power of 6? If this is not allowed than why?

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Usually (when $x$ is a positive number) $\sqrt[n]{x}$ can be treated as $x^{1/n}$, and this extends to non-integral $n$. So $\sqrt[1.5]x$ can be interpreted as $x^{2/3}$, and if $a\ge0$ we do have $\sqrt[0.5]{a^3}=a^{3×2}=a^6$.