Final answer:
The thoracodorsal nerve is innervated by spinal nerve roots C7 and C8 of the brachial plexus, which supply the latissimus dorsi muscle in the back.
Step-by-step explanation:
The thoracodorsal nerve is primarily innervated by the C7 and C8 nerve roots, as it is a branch of the posterior cord of the brachial plexus. This plexus arises from the spinal nerves C5 through T1, which reorganize to give rise to the nerves that supply the arms. Specifically, the thoracodorsal nerve provides motor innervation to the latissimus dorsi muscle, which is important for movements such as internal rotation, adduction, and extension of the arm.
The thoracodorsal nerve, also known as the long subscapular nerve, is innervated by the spinal nerve of C6, which is one of the eight pairs of cervical nerves.