Zero to the power of zero
It is determined by definition that 00 ≝ 1, as you cannot calculate it's value.
Explanation
In the figure we start with 48 balls on the outer side, and this decreases each time with 8 balls to inner side. Herein we recognize the multiplication table of 8
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0• 1• 2• 3• 4• 5• 6• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
According to this calculation the center would have 0 × 8 = 0 balls. That is not true. We have to end on 1, and therefore our formula must read
Number of balls per side = n × 8 + 0n
The correction term then results in
Side Amount 6 6 × 8 + 0 = 48 5 5 × 8 + 0 = 40 4 4 × 8 + 0 = 32 3 3 × 8 + 0 = 24 2 2 × 8 + 0 = 16 1 1 × 8 + 0 = 8 0 0 × 8 + 1 = 1
There are good reasons to determine something by definition.