What part of the hand is supplied by the radial nerve and its branches?

The back of the hand is primarily supplied by the radial nerve and its branches. The radial nerve provides sensory innervation to the dorsal aspect of the hand, which includes the skin over the back of the hand and the corresponding areas of the fingers, except for those that involve the thumb's palmar surface and the pinky finger. The radial nerve is responsible for the sensation in the areas of the hand that are not covered by the median and ulnar nerves, which supply the palmar surface and the anterior aspect of the fingers.

In contrast, the palmar surface of the hand is primarily innervated by the median and ulnar nerves. The thumb does receive some innervation from the radial nerve on its back aspect, but not for the palmar side. The pinky finger is mainly supplied by the ulnar nerve and not significantly by the radial nerve. Therefore, the correct answer highlights the area that is specifically served by the radial nerve, emphasizing the role of this nerve in providing sensation to the back of the hand.