as the title asks, is there an integer which is a perfect square, cube, fourth power, fifth power, etc until, well, it's a tenth power per say? Are there integers that are squares, cubes, and so on until it is a... Say, 100th power?
I was wondering because I saw this olympiad problem which asked for a square root of a number times a cube root of the same number, in which case I thought the best way to solve this would be to think of a number that is both a square and a cube and then work out the answer manually.
A proof or explanation, or any general useful contribution, will be greatly appreciated. Thanks! :)