Write the powers of 2 in a column and keep the L2 step-down rule - each step down divides the value by the base: 2^3 = 8, 2^2 = 4, 2^1 = 2, 2^0 = 1. Next step down: 1 / 2 = 1/2, then 1/4, then 1/8. The pattern leaves no choice: 2^-1 = 1/2, 2^-2 = 1/4, 2^-3 = 1/8. And notice what those are: 1/2 = 1/2^1, 1/4 = 1/2^2, 1/8 = 1/2^3. That is the definition the pattern forces: a^-n = 1/a^n - a negative exponent moves the power into a denominator (equivalently: it takes the reciprocal of a^n). The restriction, explained: a != 0. At base 0 the pattern's engine - divide by the base at each step - is division by zero, and the definition would read 0^-1 = 1/0. There is no value, because division by zero is undefined. And the sign warning, said plainly: the minus on the exponent does not make the value negative. 2^-3 = 1/8, a small positive number. The minus sign is about position, not sign.

Evaluate 3^-2 -> 1/9 (pattern: 3^0 = 1, step down twice: 1/3, then 1/9; equivalently 1/3^2)