Negative Exponents for Dummies (Math Week 4)

Negative exponents

One thing we've realized here at the Antisocial Network is that you can always tell when a freelancer is just rewording material from an authoritative (or somewhat authoritative) source is that key concepts are left out. Perhaps the freelancer didn't look beyond one source; perhaps the source didn't mention the concept. Around here, though, we think that someone who is "informing" his or her reader should be doing so from expertise; not from having been taught how to reword someone else's thoughts. Unfortunately, the latter is often the case with the contributors at eHow.com... Take, for instance, Charlotte Johnson (again!), whose Masters in Education apparently wasn't for math, as she amply demonstrates when writing "How to Raise a Number to a Negative Power"¹ for the good folks at Demand Media (home of questionable information).

As Char (may we call you "Char," Char?) explains, sort of, 

"The number of times that you multiply the value times itself is indicated by the exponent. An exponent is another term for a 'power.' If you have a number that is raised to a negative power, you must solve this type of problem by completing a process known as the 'multiplicative inverse'...

Ummm, Char, "multiplicative inverse" isn't a process, it's a quantity. Although you don't mention it -- perhaps because you don't know this, perhaps because your source didn't mention it, perhaps because your source mentioned it and you didn't think it important; but most likely because you don't know jack about math -- a quantity's multiplicative inverse is also known as its reciprocal.

Johnson gives exactly one example and, of course, she gets it wrong. We kid you not!!! "Write the number with its exponent. Remove the negative sign from the exponent. For instance, if you have 2^-3, you would rewrite this as 1/2^8. Well no, Char, if you remove the negative sign from the exponent in the expression 2^(-3) (see how we used the parentheses to make it easier to read? watch and learn!), you don't get 1/2^8 -- you get 2^3, you ignoramus! that's not to mention that you don't "remove a negative sign," you take an absolute value.  OK, so you skipped a couple of steps and hosed the answer, but these morons still paid you for this crap? How do we get a gig like that?! Whatever... after thrashing around for a while, Johnson finally gives the right answer, probably because she merely copied it: "Multiply the number times itself the number of times as indicated by the exponent. In this example, you would multiply 2 times itself three times to get 8. Therefore your answer to 2^-3 would be 1/8.

See what we mean by skipping a couple of steps? Oh, and by the way, if you "multiply 2 times itself three times"; you don't get 8 – you get 16...

In reality, the answer to this question is simple: A number raised to a negative exponent generates the reciprocal of the number raised to the absolute value of the exponent: X^(-3) = 1 / (X^3).

Johnson gave a specific answer to a general question by concentrating on 2, messed up the instructions, and clearly did not know the subject matter well enough to generate an answer on her own to what is really a very simple question. Is it any wonder we're naming her the Dumbass of the Day?

¹ The original was moved to Sciencing.com and then deleted by Leaf Group, but can still be accessed using the Wayback machine at archive.org. Its URL was    ehow.com/how_8391316_raise-number-negative-power.html

copyright © 2016-2022 scmrak

MM - ALGEBRA