Germany was actually pretty accepting of the Japanese despite the whole Aryan master race thing. In fact, Hitler himself stated:

"Pride in one's own race – and that does not imply contempt for other races – is also a normal and healthy sentiment. I have never regarded the Chinese or the Japanese as being inferior to ourselves. They belong to ancient civilizations, and I admit freely that their past history is superior to our own. They have the right to be proud of their past, just as we have the right to be proud of the civilization to which we belong. Indeed, I believe the more steadfast the Chinese and the Japanese remain in their pride of race, the easier I shall find it to get on with them"

Due to this the Japanese were granted an "Honorary Aryan" status by the Germans, meaning while they were not of Nordic roots, they displayed enough qualities of Nordic/Germanic origins to be suitably Aryan. Japan at the time was the most western nation in east Asia and was considered properly western by most of the world's countries, as Japan had undergone westernization nearly 70 years ago with the Meiji Restoration.

It's a common misconception that the Axis wanted to conquer the world, but this isn't the case. I don't know much about Japan, but Hitler never sought world domination. His goal was to create a massive German empire encompassing eastern Europe and western Russia. The natives would mostly be killed, with some portion kept for slave labor, and German families would settle and farm this new frontier. The resources this new empire would provide, and the population it would support, would le Germany compete in the long term with the US, the British Empire, and the French Empire. No real conflict with Japan here, who (as far as I know) were also fighting to secure the resources to be the dominant power in the Pacific.

Any good book on Nazi Germany will cover this grand strategy, which was known as Generalplan Ost. I'll recommend Kershaw's biography of Hitler.