Can we write "fractional root" symbol in math?

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Fractional exponents are legit but I have never seen fractional roots, so I just wonder if we can write fractional roots such as this:

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It sometimes can be convenient to think about too.

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We do have fractional roots but, I write it like - $$x^{\frac{a}{b}}=C \to x=C^{\frac{b}{a}}$$ But anyways there are a lot of ways you can represent math symbols and I can't find anything wrong in your representation too.