What is the power to the tenth square?

Your question is meaningless.

Lay two buttons on the table. Lay two more so you have two rows of two buttons per row. Now count all the buttons: four. So four is a square number, and the root of four is two. Do it with three rows of three buttons per row and you get nine buttons total: nine is a square number and the root of nine is three. Now you begin to see what "square" means.

You could do this project with two stacks of two buttons per row and two rows and then you would get a cube with eight buttons in it, demonstrating that eight is a cube number and the cube root of eight is two, and so on, but it gets to be impossible with large numbers or fractional numbers. But at least now you see what a power really means.