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2. Exponentiation - Wikipedia

   en.wikipedia.org/wiki/Exponentiation

   Exponentiation with negative exponents is defined by the following identity, which holds for any integer n and nonzero b: =. [1] Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (). [22]

3. Falling and rising factorials - Wikipedia

   en.wikipedia.org/wiki/Falling_and_rising_factorials

   For example, () = = is the number of different podiums—assignments of gold, silver, and bronze medals—possible in an eight-person race. On the other hand, x ( n ) {\displaystyle x^{(n)}} is "the number of ways to arrange n {\displaystyle n} flags on x {\displaystyle x} flagpoles", [ 8 ] where all flags must be used and each flagpole can ...

4. Reciprocal rule - Wikipedia

   en.wikipedia.org/wiki/Reciprocal_rule

   The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents. Also, one can readily deduce the quotient rule from the reciprocal rule and the product rule .

5. Exponentiation by squaring - Wikipedia

   en.wikipedia.org/wiki/Exponentiation_by_squaring

   The method is based on the observation that, for any integer >, one has: = {() /, /,. If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent.

6. Power of 10 - Wikipedia

   en.wikipedia.org/wiki/Power_of_10

   The sequence of powers of ten can also be extended to negative powers. Similar to the positive powers, the negative power of 10 related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10 −[(prefix-number + 1) × 3] Examples: billionth = 10 −[(2 + 1) × 3] = 10 −9

7. Power of two - Wikipedia

   en.wikipedia.org/wiki/Power_of_two

   By comparison, powers of two with negative exponents are fractions: for positive integer n, 2 −n is one half multiplied by itself n times. Thus the first few negative powers of 2 are ⁠ 1 / 2 ⁠, ⁠ 1 / 4 ⁠, ⁠ 1 / 8 ⁠, ⁠ 1 / 16 ⁠, etc. Sometimes these are called inverse powers of two because each is the multiplicative inverse of ...