How can ionizing radiation from nuclear explosions cause cancer?

Damaging genes. Inhaling or ingesting the radioactive particles that come from the explosing is also risky -- in fact, after chernobyl, most of the problems are thyroid concerns from the iodine. People in hiroshima and nagasaki had a significant rise especially in rates of leukemia, civilians exposed to tests had less cancers long-term than many had feared.