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en.wikipedia.org/wiki/Exponentiation

If b < –1, bn, alternates between larger and larger positive and negative numbers as n alternates between even and odd, and thus does not tend to any limit as n grows. If the exponentiated number varies while tending to 1 as the exponent tends to infinity, then the limit is not necessarily one of those above. A particularly  ...

www.shelovesmath.com/algebra/intermediate-algebra/exponents-and-radicals-roots

Radicals (which comes from the word “root” and means the same thing) means undoing the exponents, or finding out what numbers multiplied by themselves comes .... We'll do this pretty much the same way, but again, we need to be careful with multiplying and dividing by anything negative, where we have to change the ...

www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L1_T3_text_final.html

Use the laws of exponents to simplify expressions with rational exponents. ... Radicals and fractional exponents are alternate ways of expressing the same thing. ... These examples help us model a relationship between radicals and rational exponents: namely, that the nth root of a number can be written as either or .

www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-19_RESOURCE/U16_L2_T2_text_container.html

Making sense of a string of radicals may be difficult. One helpful tip is to think of radicals as variables, and treat them the same way. Let's start there. Thinking about Radicals as Variables. Radicals can look confusing when presented in a long string, as in . How do you simplify this expression? (It is worth noting that you will ...

www.khanacademy.org/math/algebra/rational-exponents-and-radicals/rational-exponents-and-the-properties-of-exponents/v/fractional-exponent-expressions-2

You have to be real careful here: if you had a regular fraction squared, e.g. 2/3, then sure you'd do (2/3)*(2/3). But here, the fraction is not a base you have to raise to a power; it is actually an exponent! That means that what you have to square is not 2/3, it's the whole (r^(2/3)). And the way you do that is by multiplying the two ...

www.purplemath.com/modules/radicals2.htm

As you can see, simplifying radicals that contain variables works exactly the same way as simplifying radicals that contain only numbers. We factor, find things that are squares (or, which is the same thing, find factors that occur in pairs), and then we pull out one copy of whatever was squared (or of whatever we'd found a  ...

tutorial.math.lamar.edu/Classes/Alg/Radicals.aspx

As we saw in the integer exponent section this does not have a real answer and so we can't evaluate the radical of a negative number if the index is even. Note however that we ... Also note that while we can “break up” products and quotients under a radical we can't do the same thing for sums or differences. In other words , ...

magoosh.com/gre/2016/positive-and-negative-square-roots-on-the-gre

Sep 7, 2016 ... This is a very rare topic on the GRE — you might be able to take 10 GREs and not see fractional exponents once. That's just to put the relative importance in context. Every standard high school math book on the planet defines (a)^(1/2) exactly the same way as “a” under a radical — both mean positive root ...

blog.mrmeyer.com/2015/if-exponent-rules-are-aspirin-then-how-do-you-create-the-headache

Jul 1, 2015 ... Although a detailed discussion of why either of those two series behave the way they do probably isn't that interesting to most kids, the idea that most .... I typically take a while with kids 'unlearning' radical expressions when we get to calculus anyway, so I feel the same was as you regarding necessity.