Specific POA authorising brother to sell property can be registered in Gujarat since you are residing in Gujarat 

The Power of Attorney for the property situated in Karnataka can be registered in Gujarat or Karnataka. Since you live in Gujarat and the property is in Karnataka and you are unable to travel to Bangalore, you can authorise your brother through POA and get the POA registered in Gujarat, for your brother to act on your behalf in Bangalore to conclude the transaction.

POA and registration of sale deed through POA can be done only in the local of jurisdiction of Sub-Registrar, in your case it the town in which property is situated in Karnataka. It cannot be done from Gujarat.  Even for registration of POA it the local Sub-Registrar who has power.

The power of attorney deed can be registered in the place where the principal is residing.

There's no necessity to register the deed where the property is located.

You need to register POA in Karnataka where the property comes under a sub-registrar office area city wise.

You can get the POA drafted anywhere In India.

Registration of POA can be done in Gujarat or Karnataka.

It's better that you register the POA at the place where property is situated 

The PoA can be drafted (by a competent lawyer), executed and registered in Rajkot, Gujarat, where you live. It needs to be registered with the registrar of assurances having jurisdiction over your place of residence there. Once it is duly registered, it is valid throughout India, and as such, will be legally valid for selling your property in Karnataka.

Dear client, A POA should be registered at the Office of the Sub-Registrar along with 2 attesting witnesses. Generally, documents such Passport, AADHAR Card, passport size pictures, etc. of both the parties is required for registration. Power of attorney can be drafted and attested in any part of India where the people belongs in your case it can be registered either in Karnataka or Gujarat

- Since, the property is based in Karnataka , then for selling the same you can give POA to your brother if you are unable to go there for the same .

- The POA can be registered from the office of the registrar from the place of your residence i.e. Gujrat.