Tide, I really don't know what to do with spherical coordinates. Maybe you can show me.
But, I found another way..Here it is:
nabla x r^4r =
= r^4rotr - r x grad r^4
= 0 - r x dr^4/dr r/r
= - r x dr^4/dr r/r
= - dr^4/dr 1/r rxr
= 0
btw. bold are vectors; curl=rot; nablaxnablaf=0...