The Montessori school I went to didn't have an abacus for us to use, but to your point, the physical representations of 10^1 (a row of 10 beads), 10^2 (a 10x10 square of beads), and 10^3 (a 10x10x10 cube of beads) using beads helped me understand exponents much more quickly. Unfortunately we did not have a 10x10x10x10 tesseract of beads.