Looking for a book from 25 ish years ago, Aliens mined Earth and made Humans their slaves, but a human bombs the alien homeworld,

Question

The story is based on a future Earth that has been destroyed. Humans have been reduced to a primitive race and the Earth has been mined by an alien race that uses the humans as slaves to work in the mines. The aliens cannot breath our air and our air is explosive when mixed with their air. One of the humans is captured by one of the aliens and kept as a pet. That human is taught all of the aliens knowledge via a computer that blasts the knowledge into his head. The human then devises away to destroy the alien home world with a bomb built like a casket.

Answer 1

This is L. Ron Hubbard's infamous book Battlefield Earth (1982).

Wikipedia's notes on the setting:

In the year 3000 AD, the Psychlos, an alien race, have ruled Earth for a millennium. The Psychlos discovered a deep space probe (suggested to be Voyager 1) with directions and pictures mounted on it and the precious material, gold, which led them straight to Earth.

Psychlos stand up to 9 feet (2.7 m) tall and weigh up to 1,000 pounds (450 kg). They originate from Psychlo, a planet with an atmosphere radically different from Earth, located in another universe with a distinct set of physical laws characterized by a lack of elements that are radioactive. Their "breathe-gas" explodes on contact with even trace amounts of radioactive material, such as uranium. The Psychlos have been the dominant species across multiple universes for at least 100,000 years.

After one thousand years, humanity is an endangered species numbering fewer than 35,000 and reduced to tribes in isolated parts of the world while the Psychlos strip the planet of its mineral wealth.

Quoting the plot summary from Wikipedia:

The novel follows Jonnie Goodboy Tyler, a young man in one such tribe who lives near the ruins of Denver in the shadow of the Rocky Mountains. Depressed by the recent death of his father and both the lethargy and sickness of the surviving adults in his tribe, he leaves his village to explore the lowlands and to disprove the superstition long held by his people of monsters in those areas.

On a brief excursion to the ruins of Denver, Terl, Psychlo chief of mine site security, encounters and captures Jonnie. After forcing Jonnie to learn the Psychlo language, Terl learns that the "home office" has extended his tour of duty on Earth. Maddened by the prospect of being stuck on a minor planet in an insignificant universe, Terl schemes to take a load of gold in the Rockies for himself and escape. Uranium deposits surround the lode, making mining by Psychlos impossible, forcing Terl to resort to using humans as forced labor.

Terl orders a fellow Psychlo named Ker to train Jonnie to use Psychlo machinery. Ker, markedly different both in height (7 feet (2.1 m) tall) and in temperament from other Psychlos, trains Jonnie as ordered, but the Psychlo and Jonnie also become friends. During their exchanges, Jonnie learns how the Psychlos initially conquered Earth, mainly by sending a large armored drone into Earth's orbit, known as a Gas Drone, which orbited the planet, gas bombing all major cities and killing billions. Humans fought back, launching attacks against the drone with first conventional and then nuclear weapons, but the drone was unharmed. Eventually, the last of the human leaders suffocated inside bunkers, the air vents sealed to prevent poison gas from entering. Terl and Jonnie travel to Scotland, where Jonnie recruits 83 Scottish people led by Robert the Fox to help with the mining. Using Terl's inability to understand English as a weapon, Jonnie plots with the Scotsmen to take back the Earth.

Months later, Jonnie and the Scots disrupt the semi-annual teleportation of personnel and other goods to Psychlo, using Psychlo technology against the Psychlos and gaining control of the planet. A year after humans gained control of the planet, other alien races arrived and orbited the Earth. Threatened by these races, Jonnie simultaneously opposes a race of intergalactic bankers seeking to repossess the Earth for unpaid debts. The security and independence of humanity once again threatened, Jonnie eventually discovers that Psychlo was destroyed by Jonnie and the Scots, mainly by transporting radiative material into the Psychlo atmosphere which caused a chain reaction, and that all other Psychlo facilities throughout the universes were also destroyed, effectively dooming the Psychlos to extinction. He then works out a way to prevent the repossession of Earth.

With the help of an aged Psychlo mathematician, Jonnie learns about Psychlo math and how the Psychlos protected their technology. Humans begin to rediscover their history, and with the Earth secure and the human population growing, a middle-aged Jonnie takes supplies and quietly slips away to the Rocky Mountains. He becomes a figure of legend.

Just to clarify a few points in your recollection, since I recall this novel far too well for one I hated and haven't read in 40 years:

• Humans are used as slaves only in the Colorado Rockies, where Terl is trying to get at a gold deposit that is otherwise inaccessible to the Psychlos because of nuclear mines buried to protect access to NORAD headquarters.
• It's not a bomb built like a casket, it's an actual shipment of caskets of Psychlos who had died on Earth being sent home. (I forget the number, but there are several of them.) Jonnie and his team replace the bodies with hydrogen bombs (how they still work after 1000 years is unexplored) and at the time of teleportation, Jonnie rides in on his horse to manually set the fuses.
• The Wikipedia summary is a bit misleading; it's not simply radioactive material that causes the explosion, since the receiving teleport station on the Psychlo homeworld has shields the snap down when radioactivity is detected to prevent exactly that. However, while the shields hold against multiple H-bombs, there is no shield underneath the teleport platform, and the H-bombs vaporise enough rock underneath (which is honeycombed with mining tunnels) to release the explosion (and the radioactive fallout) into the atmosphere.