Long-term, the bombings of Nagasaki and Hiroshima showed the world the power of an atomic weapon. The Soviet Union distrusted America for using the weapon to end the war and the Russians started to capture nuclear scientists all over their sector of Germany in order to work on their own version of "the bomb." After the Soviets developed nuclear weapons, both sides sought to increase their nuclear capacity, because in a nuclear war, it was understood that whoever fired first would win, and that nuclear warfare would most likely cause destruction all over the world. The Soviets and Americans soon developed bomber fleets, intercontinental ballistic missiles, and nuclear submarines in order to bomb cities. Politicians in both countries used nuclear preparedness as a rallying cry, and John F. Kennedy was elected in 1960 because the previous administration created an alleged "missile gap" which did not exist. The Cuban Missile Crisis was sparked by the threat of a nuclear war, and it opened up negotiations between the White House and Kremlin. The United Nations took an active role in deciding which nations could have nuclear weapons after the fall of the Soviet Union, and this fear of nuclear proliferation has meant economic sanctions for North Korea and regime change in Iraq.
There were some peaceful things to come out of the nuclear arms race, however. Scientists developed nuclear power, and "nuclear" became a positive buzzword of the 1950s. The ideal family was said to be "nuclear" if it had a mom, dad, and children. Through developing intercontinental ballistic missiles, scientists also developed the rockets needed to go into space. America poured more money into teaching children math and science in order to create a new generation of scientists.
Short-term results of the bombing are that Nagasaki and Hiroshima were wiped off the face of the Earth, thousands died due to radiation poisoning and the blast itself, and imperial Japan surrendered, thus making unnecessary the invasion of Japan slated for November 1945. America became the sole occupier of Japan, tried its war criminals, and assisted with the creation of the new Japanese constitution that was more liberal than America's at the time.