Polynomials

Please explain is (4x+9)^3/2 is a polynomial or not in my book it is written is written that the above (4x+9)^3/2 expression is not a polynomial. But i think (4x+9)^3/2 is a polynomial because when i put any value of x has power 1 in the expression which is whole number it does not have the power which is not a whole number so it is a polynomial right please tell what is correct... Thank you....

@AnkurGoyal For a function to be polynomial its variable power should be non negative INTEGER but here it is not integer.