Playing around with numbers and I realized this..

(x^2)_x = { (10^2 iff x ≤ 7 ), (x^2 iff x≥ 8) }

Why is this? ( y_x means y converted into base x )

It also works changing the exponent to 3, or 4, or 5, etc.

(x^3)_x = { (10^3 iff x ≤ 7 ), (x^3 iff x≥ 8) }

What is special about the numbers below 8??

Rule: (x^n)_x = { (10^n iff x ≤ 7 ), (x^n iff x≥ 8) }