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Gary Wheeler wrote: A math class. With no books. Western civilization is doomed.
Soooo right. It's a nightmare, with hastily bodged-together curriculum with no backup at all. Makes me crazy, and my kid's just in elementary school.
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I haven't searched, but you could try looking for it in Latex and seeing if that offers any clues via name/documentation etc.
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My wife and I both searched. Even Wolfram seemed to just shrug.
We wouldn't be surprised to find that it's the wrong symbol. Or some cockamamie new "common core"  thing.
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My guess, based on the context of the formula, would be that it means "simplify". Now, if your child is in a graduate course on non-associative algebra, the answer may be different.
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Sure it's not a printing error? A multiplication sign that is messed up? That would make the most sense to me at least.
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This is in line with my thinking. I've seen multiplication represented by an 'X', an '*' (asterisk), a dot, and an open dot (circle). Maybe they were going for a dot or open dot, but the character set the printer used didn't have an exact match. The anti-clockwise arrow may have been the best fit. (Why they didn't replace it with a common alternative like 'X' or '*' is anyone's guess...)
Of course then you have to ask what business the printer has printing math books without a sufficient character set... But that's another conversation entirely...
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Have not found it anywhere though have tried even image search, definitely not standard math symbol. Its either printing error or an individual attempt to map a shaky concept into self created image.
Do
Read();
Research();
Experiment();
UnTil You Inspire!
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Never seen it either, but it might be an indication of an iteration of some kind?
ask teacher 
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I graduated math but I 've never seen this symbol. Maybe it is Operation defined before question.
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The rational exponents can only simplified if the symbol is a division. If you multiply 12/5 * 3/5 you get 36/25 which cannot be simplified. The other way around 12/5 / 3/5 = 4 makes a lot more sense. Same for the other expression.
Josef Schroettle
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Except that a multiplication symbol there would mean you add the exponents together, not that you multiply them.
For example: c^2 x c^3 equals c^5, not c^6.
Therefore, if it is multiplication, you will actually be doing: 12/5 + 3/5 which is 15/5 which simplifies to 3.
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I thought when you multiplied the same variable with two different exponents together, you just add the exponents. So..
c^(12/5) * c ^(3/5) ==> c^(12/5 + 3/5) ==> c^(15/5) ==> c^3
x^(3/4) * x^(9/2) ==> x^(21/4), or x^(5 1/4
Looks to me like the counter-clockwise arrow is a typo -- meant to be a dot for multiplication, but they used the wrong glyph, and the proof reading quality control these days is left as an exercise for the student.
We can program with only 1's, but if all you've got are zeros, you've got nothing.
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This is most likely a Unicode error. I think the "vertically middle dot" was meant to be printed out. Do you have other exercises you could relate to ?
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I think that's the "turn around and ask the smart kid hiding in the back row for the answer" symbol.
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If the symbol is a typo for multiplication #13 become c^3, #14 not so clean x^(21/4)
You would have to figure out what the symbol is a substitute for.
Brent
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Hey!
Thirty six days to the first of April!
(no?)
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This might not help at all but makes you feel less guilty. I work now 20 years in Reinsurance and develop pricing tool, have a degree in Electronics and Economics. My work colleagues, who are by nature, all mathematicians and specialist in the field of actuarial science. Some have PHD's and other degrees I cannot even pronounce. However, I haven't seen this symbol in my entire career, and that's frustrating!
Could it mean to find a divisor to get from c^12/5 to c^3/5? Have a look here on Wolfram https://www.wolframalpha.com/input/?i=(c%5E(12%2F5))+%2F+(c%5E(9%2F5))
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I haven't taken a math class in 30 years, but 30 yrs ago, I took a lot of them. Even so, the algebra problems your kid is doing hasn't changed much since the 17th century.
Find the earliest reference in the book, or perhaps even inside the cover. I strongly suspect the author has minted his own notation. In context, it looks like you're supposed to replace the squiggly with another standard symbol, such as < etc.
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My approach would be:
Khan Academy .org
Start with the book sections you child is covering.
Use the contextual clues from the types of problems being solved.
(This would be the Chapter topic, and the section topics, and problem heading (solve for x))
Start there with a broad scan.
At the very top of the site is a search. I usually can find anything a student is working on.
Also helps to know know what level of algebra.
Finally, in most math books these days, even the ONLINE versions, the symbols are introduced in the sections the kids never read at the front of the section. Usually as an EXAMPLE problem!
HTH
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Your machine probably just doesn't support the original font, so it produced this other character from whatever font it could provide. Check the course requirements for which font you need to install.
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From the context I assume it represents 'the reciprocal of'. So with the implied multiply operator we'd get
13) 4
14) 1 / 3x^2
But what do I know - I'm 65!
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Oh, now that's an idea. Thanks. 
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It may be a good idea but my answers are wrong as I mis-read the two questions. If I'm right about the reciprocals bit then the correct answers I reckon are:
13) c^4 14) 1 / x^6
(I'm happy to sit at the back of the class)
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If your kid's been out, how did he get the homework? Did he download it from a webpage or some such? If so, it might be a font mismatch between the teacher's computer and yours.
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