1. Power addition rule:
If two powers have the same radix (called a), they can be added. In this case, the exponents (called n and m) will remain the same, while the cardinality will remain the same. The result is a new power, its base is still a, and the exponent is the sum of the exponents of the original two powers. Namely:
Answer? + a? = a^(n + m)
2. Power subtraction rules:
Similarly, if two powers have the same radix (called a), they can be subtracted. In this case, the exponents (called n and m) will remain the same, while the cardinality will remain the same. The result is a new power, its base is still a, and the exponent is the difference between the exponents of the original two powers. Namely:
Answer? - a? = a^(n - m)
These rules are valid for any real number a and integers n and m, as long as the cardinality is the same. When the cardinality is different, the power cannot be added or subtracted directly.