Most problems require the student to simplify the final answer and in many context the meaning is obvious: For example, $3/9$ should be simplified to $1/3$ and $\sqrt{16}$ should be simplified to $4$.
However, how about the answer $$6\left(\frac{2}{3}\right)^{1/5}?$$
This same answer can be equivalently written as $\sqrt[5]{5184}$ or $2^{6/5}\cdot 3^{4/5}$, etc. Which one(s), if any, is considered as "simplified as much as possible"?
Rigid criteria for simplification seem to me largely a bad idea if they are not motivated by contextual considerations. The idea that $\sqrt{2}/2$ should be preferred to $1/\sqrt{2}$ struck me as unmotivated when I was a student, and now seems to me problematic to motivate. The situation is different with respect to writing rational numbers or rational functions. In both cases there is a canonical simplification, that in which the numerator and denominator are relatively prime.
In a particular context it might make more sense to write $6(2/3)^{1/5}$ than to write $2^{6/5}3^{-4/5}$. It might be that the $6$ in front and the $2/3$ have different extra-mathematical origins, e.g. the $6$ counts something and the $2/3$ reflects a ratio of measurements, and it's just an accident that both are expressible in terms of powers of $2$ and $3$. In a purely mathematical context there are no such considerations, but then still one might prefer one form or the other (I find $6(2/3)^{1/5}$ easier to interpret at a glance than $2^{6/5}3^{-4/5}$).
Returning to the $\sqrt{2}/2$ versus $1/\sqrt{2}$ example, imagine we are working in the field $\mathbb{Q}[\sqrt{2}]$. Then, in fact, we can always write an element of $\mathbb{Q}[\sqrt{2}]$ in the form $a + b\sqrt{2}$ with $a$ and $b$ rational. In this context there is a normalized expression, and it would be $(1/2)\sqrt{2} = \sqrt{2}/2$ rather than $1/\sqrt{2}$ (working in $\mathbb{Q}[\sqrt{2}]$ we have to prove (!) that $\sqrt{2}$ is invertible before we can give sense to $1/\sqrt{2}$ - as a shorthand for its inverse in this field extension of $\mathbb{Q}$). On the other hand, if we are working in the field $\mathbb{R}$, then $1/\sqrt{2}$ is directly the expression for the inverse of $\sqrt{2}$ qua element of $\mathbb{R}$. It's that thing that gives $1$ when we multiply it by $\sqrt{2}$ which we know exists from when we constructed the real field (when did we do that?). The conceptual apparatus necessary to make such distinctions/motivations comprehensible (in this case amounting to distinguishing between the inverse of $\sqrt{2}$ in the field $\mathbb{R}$ and its inverse in $\mathbb{Q}[\sqrt{2}])$) is simply not available to (all but a very few highly exceptional) students in primary education where these things are taught. Insisting on the use of a "canonical" form without providing motivation for what makes it canonical ("canonical" is always with respect to some background context) has the feel of authoritarian dogma. This can alienate students, particularly those with a more creative or curious mindset.
Absent some context that motivates preferring one or another simplified form, demanding one or the other such form seems to me typical of the sort of teaching that turns students off from mathematics. What is arbitrary should generally be avoided.
I would say the canonical answer for what constitutes 'simplified as much as possible' is whatever the exam board says it is.
'Simplify' isn't a mathematical function. It is a pedagogical instruction trying to require students to make use of a selection of mathematical equivalences that they are expected to know. However, it is too vague a term to make clear exactly which such equivalences are expected in a particular case.
Consider
$$\frac{(x-1)(x-2)^2}{(x-2)(x+2)}.$$
A student might reasonably realise they should cancel the factor on the top with that on the bottom, when it's written like this. But if it was presented as
$$\frac{x^3-5x^2+8x-4}{x^2-4}$$
it is far less clear that cancelling can reasonably be expected. Also, whether the final answer should be factorised or expanded is dependent on context.
So I would say that the instruction to 'simplify as much as possible' should only be used in situations where it is clear to the students what that means. Otherwise, more explicit instructions should be used (or more than one answer judged as correct).
There is a theorem which says that it is impossible to decide the equivalence of two elementary functions syntactically. So there is not, and cannot, be a uniquely defined "simplest form" for a given expression.
http://inst.cs.berkeley.edu/~cs282/sp02/readings/caviness.pdf
I suggest to do a Google search and at least read a couple pages that give the classical rules for simplifying radical expressions. You may still have some critique but will at least know what you are criticizing. Question as stated shows lack of familiarity with basics.
P.s. $2 \sqrt[5]{162}$ is the classical answer.
