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1. Recall: If n is a positive integer, then
and, if .
4. Definition of : If is a real number , (that is b ≥ 0 if n is even), then .
Note that the denominator of the exponent becomes the index of the radical.
5. Definition of : If m and n are positive integers with m/n in lowest terms, then
(This definition seems reasonable because we want
6. If all indicated roots are real numbers, then
8. Definition of : If is a real number and b ≠ 0, then
9. Be careful with minus signs . Recall that a negative exponent does not make the expression negative.
10. Rules for Rational Exponents: If r and s are rational numbers and a and b are real numbers for which the indicated expressions exist, then
12. Caution: For example