1. MTH 091 Section 10.2 Negative Exponents

2. Negative Exponents? In our previous work with exponents (Section 10.1), all of the exponents were counting numbers. We now extend our discussion to exponents that are negative. Our general philosophy is to apply rules that will make the exponents positive.

3. More Rules If your exponent is negative, flip it over and make the exponent positive. If you are dividing with like bases, keep the base and subtract the exponents

4. Beware of Negative Bases! A negative base does not need to be flipped over. Only having a negative exponent requires making a change.

5. An Order of Operations, of Sorts 1.If you have outside exponents, distribute them over parentheses. 2.Don’t try to raise a number to a negative exponent! 3.Factors with negative exponents MOVE (bottom-to- top or top-to-bottom). 4.Simplify the numerator and denominator separately. Raise coefficients to powers. 5.If you have like bases on the top and bottom, subtract. Reduce or divide coefficients.

6. Examples

7. More Examples

8. Still More Examples