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Exponent Properties

Exponent Properties. For all real numbers n , m , x , y. (except that 0 0 is undefined, and denominators can never be zero). Exponent Properties. Exponent Properties. Warning. Derivations. We know that. n factors. If n is a positive integer. Derivations. Consider. When n > m.

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Exponent Properties

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  1. Exponent Properties • For all real numbers n, m, x, y • (except that 00 is undefined, and denominators can never be zero)

  2. Exponent Properties

  3. Exponent Properties Warning

  4. Derivations • We know that n factors If n is a positive integer

  5. Derivations • Consider When n > m

  6. Derivations • For Example

  7. Derivations • So adopt the rule

  8. Derivations • Now suppose n = m

  9. Derivations • But we know that

  10. Derivations • And so it must be true that

  11. Derivations • Now suppose n < m, for example:

  12. Derivations • But our rule says

  13. Derivations • So we must conclude that

  14. Derivations • Or in general,

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