This is the 10100th most frequent Japanese word.
遥かに
"遥かに" means "far more" or "by far."
The term "遥かに" is used here to emphasize the degree to which solving the problem was simpler compared to expectations or standards.
彼はその問題を遥かに簡単に解決した。
He solved the problem far more easily.
"遥かに" is applied to indicate the significant disparity or superiority in height of the mountain, enhancing its description.
その山は遙かに高く、美しい景色を見せる。
That mountain is far taller and offers beautiful scenery.
In this sentence, "遥かに" demonstrates the substantial extent to which his talent exceeds that of his peers.