en.wikipedia.org/wiki/Exponentiation

If b < –1, b^{n}, 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.