# Integer Exponents and the Quotient Rule

1.** Zero Exponent:** For any nonzero real number a,
a^{0} =1.

2.** Negative Exponents:** For any nonzero real number
a and any

integer n,.

Note that the negative exponent does not change the sign
of the base.

(It is not a coefficient.)

3. Note that this means: , for a ≠ 0.

4. **Changing from Negative to Positive Exponents:**
For any nonzero

numbers a and b, and any integers m and n,

Note that these rules do not work if there is a sum or difference in the

numerator or the denominator.

5.** Quotient Rule for Exponents:** For any nonzero
real number a and

any integers m and n,

When dividing like bases, keep the same base and subtract
the

exponents. (You can always use the definition of an exponent and

cancel common factors.)

6. These rules are often combined. Also note that these
rules can be

combined in several correct orders.

7. See the summary of rules on pages 268 and 269.