What’s negative 2 to the fourth power? 16? -16? If you put “-2^4″ into the TI-83, you get -16. But we know that (-2)(-2) = 4 and (-2)(-2) = 4, and (4)(4) = 16. So why does the calculator give us -16?
This post is no doubt for the high schooler and not for someone addicted to the )( buttons on the calculator like I am. I parenthesize. It comes from a fear that something will go negative that should be positive. I have reminded my students more times than I can count to parenthesize, so many times, in fact, that I am more than sure that most tune me out as soon as they hear the first syllable. But still the negative raised to an even number sneaks past the best of ‘em.
The evil negative base reared its ugly head again today when I graded papers on the geometric sequence an = a1 • r^(n-1) where:
an = the value of the nth term
a1 = first term’s value
r = ratio of change (ie “doubling” would be 2)
n = the terms placement (ie: 5th term would be n = 5)
“Find a7 if a1 = 5 and r = -2.” The answer I or course got more than the correct answer was ” -320″. What should the answer be? “320″. The problem should be written out first as: 5(-2)^(7-1) to make the process clear.
At least no one gave -1,000,000 as an answer. There’s still hope!