Adiabatic or isothermal process?

I was asked a question

A piston-cylinder machine contains 1 kg of air, initially at v = 0.8 m3/kg and 290 K. The gas is
compressed in a slow frictionless process to a specific volume of v = 0.2 m3/kg and a temperature of
580 K, according to the equation pv1.5 = 0.75 (where p is in bar and v as shown). Determine the work
and the heat transfer.

i assumed it was isothermal due to a slow process but apparently it is adiabtic due to the relationship p^v1.5 = 0.75. If its ever pressure times volume to a power is a consatnt is that always going to be an adaiabtic relationnship.

It is NOT isothermal as there is a change in temperature which should be obvious.

I think you need to use 1st law of thermodynamics to show that there is no heat transfer before concluding that it is adiabatic.