The deep fibular nerve is responsible for innervating the extensor digitorum longus. This muscle sits in the anterior compartment of the leg and extends the lateral toes, aided by dorsiflexion of the foot. The deep fibular nerve is the branch of the common fibular nerve that travels with the anterior compartment muscles, supplying their motor fibers, including extensor digitorum longus, extensor hallucis longus, and the tibialis anterior. It also provides sensation between the first and second toes. The other nerves don’t fit because the tibial nerve supplies the posterior compartment and the plantar surface; the superficial fibular nerve innervates the lateral (fibularis) muscles and provides dorsum foot sensation except for the web space between the first two toes; the common fibular nerve gives off the deep branch that does the actual extensor work, but the direct innervation of the extensor digitorum longus is the deep fibular nerve.

Root levels are typically L2 to L4. These ventral rami join in the lumbar plexus to form the obturator nerve, which travels through the pelvis and exits via the obturator canal to reach the medial thigh. It innervates the medial thigh muscles—adductors such as adductor longus, brevis, and magnus (adductor part), plus gracilis and obturator externus—and provides sensation to the medial thigh. This L2–L4 range explains both the motor power to adduct the thigh and the sensory area, whereas using only L2–L3 or L3–L4 would omit part of the required contributions, and L1–L2 would not include the full L2–L4 input.

In the sole of the foot, the first lumbrical is supplied by the medial plantar nerve, a branch of the tibial nerve. This nerve specifically innervates several sole muscles, including abductor hallucis, flexor digitorum brevis, flexor hallucis brevis, and the first lumbrical. The other lumbricals (second through fourth) are innervated by the lateral plantar nerve. The tibial nerve is the parent nerve, but the precise motor supply for this muscle is the medial plantar nerve, while the common fibular nerve does not innervate intrinsic plantar muscles.

The piriformis is supplied by a dedicated branch from the sacral plexus called the nerve to the piriformis. This nerve typically arises from ventral rami S1–S2 and travels directly to the deep surface of the piriformis to provide its motor innervation. That specific nerve is named for the muscle it innervates, which is why it’s the best answer. The other nerves have different targets: the superior gluteal nerve goes to gluteus medius, gluteus minimus, and tensor fasciae latae; the inferior gluteal nerve goes to gluteus maximus; and the obturator nerve mainly supplies medial thigh muscles (adductors) and does not innervate the piriformis.

The lumbosacral trunk is formed by the ventral rami of L4 and L5, which then join with sacral plexus fibers to create a bridge between the lumbar and sacral networks. This trunk is significant because it contributes to the formation of the sacral plexus and, through that plexus, to nerves such as the sciatic nerve (which carries fibers from L4 to S3). The pudendal nerve, in contrast, arises from the sacral nerves S2–S4 and does not depend on the L4–L5 trunk. So the correct idea is that the trunk comes from L4–L5 and connects to the sacral plexus to contribute to the sciatic nerve, while pudendal nerve roots are S2–S4.