#3848. exponents and negatives warmup

Mathematics, level: Middle
Posted Sat Dec 2 08:05:25 PST 2006 by Keith Schwacha (galootey@att.net).
E Windsor Reg Sch Dist, E Windsor, NJ USA
Materials Required: none
Activity Time: < 5 min
Concepts Taught: math notation

Just a warmup - can be used in high school as well. I see that most math textbooks don't mention this notation. It's not part of the "PEMDAS" order of operations that the students are taught. It's good for a "Do Now" activity.
Procedure: (on board or overhead): Evaluate the following:
3^2 (-3)^2 -(3^2) x-3^2 -3^2

Most students will answer: 9, 9, -9, x-9, and ???
For the last one some will say 9 and some will say -9. Show them that it must be -9 by the following example:
Do you all agree that the previous expression "x-3^2" simplifies to x-9? What happens if we make x=0? You get -9 as your answer. Well, if x=0 then the expression x-3^2 is the same as -3^2. The answer should be -9.
Summary: When there are no parentheses and you are raising a negative number to a power, you raise the number to the exponent first, then apply the negative sign.