Negative Exponents
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Negative Integers as Exponents:

For any nonzero real number raised to a negative integer, take the reciprocal of the number and
change the sign of the exponents. Image261.gif (1048 bytes)

Remember: Cross the line, Change the sign. When you have negative exponents, change the problem to a fraction, if not, by dividing by 1. If the variable/number with the negative exponent is on the top, then move the variable/number to the bottom and change the negative exponent to positive exponent. If the variable/number with the negative exponent is on the bottom, then move the variable/number to the top and change the negative exponent to positive exponent.



Example:

Express with positive exponents then simplify.

Question Rewrite Cross the line change the sign Simplify
Eq10010.gif (146 bytes) Eq10011.gif (205 bytes) Eq10012.gif (187 bytes) Eq10013.gif (163 bytes)
Eq10014.gif (149 bytes) Eq10015.gif (210 bytes) Eq10016.gif (191 bytes) Eq10017.gif (189 bytes)
Eq10018.gif (143 bytes) Eq10019.gif (207 bytes) Eq10020.gif (185 bytes) Eq10020.gif (185 bytes)
Eq10021.gif (170 bytes) Eq10022.gif (235 bytes) Eq10023.gif (188 bytes)    only x is raised to -7. Eq10023.gif (188 bytes)
Eq10024.gif (236 bytes) Eq10025.gif (316 bytes) Eq10026.gif (183 bytes) Eq10026.gif (183 bytes)