Any number raised to a fraction just means that you take the number to the power of the numerator of the fraction and then root it by the denominator of the fraction.
In [tex]\frac{1}{4}[/tex], we raise 624 to [tex]1[/tex] and then root it by [tex]4[/tex] which gives:
[tex]\sqrt[4]{624^1}[/tex] = [tex]\sqrt[4]{624} =[/tex] approximately [tex]5[/tex] as [tex]5^4[/tex] is [tex]625[/tex].
[tex]4.997[/tex] :D