Please Google it before saying anything, and I want proof of whatever you'll reply here.
The Korean Provisional Government was a government-in-exile that opposed the colonial rule of the Korean peninsula by the Japanese - so they most certainly were not part of the Axis powers in the 1930s and 1940s.
The Provisional Government was located in China, and so received some recognition there. They were quite a fractious bunch - with some courting support from the Chinese Nationalists, others from the USA and Western Europe, and others from the USSR.
The Provisional Government was able to coordinate Korean resistance against the Japanese and formed the Korean Liberation Army - although, the first major assault (supported by the US Office of Strategic Services - the CIA precursor) against the Japanese was not enacted because of the surrender of Imperial Japan.
So - the Provisional Government was aligned with Allied forces, but it doesn't seem to have been a formal relationship.
It doesn't look like it.
The Provisional government of the Republic of Korea was formed in April, 1919 and based in Shanghai and Chongqing.
The government did not gain formal recognition from world powers, though a modest form of recognition was given from the Nationalist Government of China and a number of other governments, most of whom were in exile themselves.
I take it world powers would refer to either the Allies and the Axis powers.
The bottom line answer would be neither.
The provisional govt. was definitely not part of the Axis powers:
...bringing together many if not all Korean resistance groups in exile. The government duly declared war against the Axis powers Japan and Germany on December 9, 1941,
But was also not officially a member of the Allies:
The government's goal was achieved with Japanese surrender on September 2, 1945, but they were not approved by other governments as a member of allied nations, who signed peace treaty with Japan in San Francisco.
All quotes from the wiki page, all emphasis mine.