I would have thought that combine(..., radical) would do it, but that only handles factors with the same exponent:

> combine(2^(7/8)*3^(1/4)*35^(1/8)/z, radical);

1/z*3^(1/4)*4480^(1/8)

Rather a kludge, but you can do this:

> combine(subs(3=9^(1/2),%),radical);

1/z*40320^(1/8)

I would have thought that combine(..., radical) would do it, but that only handles factors with the same exponent:

> combine(2^(7/8)*3^(1/4)*35^(1/8)/z, radical);

1/z*3^(1/4)*4480^(1/8)

Rather a kludge, but you can do this:

> combine(subs(3=9^(1/2),%),radical);

1/z*40320^(1/8)

Yes, you can.  For example:

> PowerOfSet:= proc(S::set, n::posint) 
     local T,j;
     uses combinat;
     T:= cartprod([S$n]);
     [seq(T[nextvalue](), j = 1 .. nops(S)^n)];
   end proc;

  add(f(op(v)), v = PowerOfSet({0,1,2}, 3));

f(0,0,0)+f(0,0,1)+f(0,0,2)+f(0,1,0)+f(0,1,1)+f(0,1,2)+f(0,2,0)+f(0,2,1)+f(0,2,2)+f(1,0,0)+f(1,0,1)+f(1,0,2)+f(1,1,0)+f(1,1,1)+f(1,1,2)+f(1,2,0)+f(1,2,1)+f(1,2,2)+f(2,0,0)+f(2,0,1)+f(2,0,2)+f(2,1,0)+f(2,1,1)+f(2,1,2)+f(2,2,0)+f(2,2,1)+f(2,2,2)

Yes, you can.  For example:

> PowerOfSet:= proc(S::set, n::posint) 
     local T,j;
     uses combinat;
     T:= cartprod([S$n]);
     [seq(T[nextvalue](), j = 1 .. nops(S)^n)];
   end proc;

  add(f(op(v)), v = PowerOfSet({0,1,2}, 3));

f(0,0,0)+f(0,0,1)+f(0,0,2)+f(0,1,0)+f(0,1,1)+f(0,1,2)+f(0,2,0)+f(0,2,1)+f(0,2,2)+f(1,0,0)+f(1,0,1)+f(1,0,2)+f(1,1,0)+f(1,1,1)+f(1,1,2)+f(1,2,0)+f(1,2,1)+f(1,2,2)+f(2,0,0)+f(2,0,1)+f(2,0,2)+f(2,1,0)+f(2,1,1)+f(2,1,2)+f(2,2,0)+f(2,2,1)+f(2,2,2)

Something like this?
 

> < < 1 | 2 | 3 | `...` >, < 2 | 3 | 4 | `...` >>;

                         [1    2    3    ...]
                         [                  ]
                         [2    3    4    ...]

Something like this?
 

> < < 1 | 2 | 3 | `...` >, < 2 | 3 | 4 | `...` >>;

                         [1    2    3    ...]
                         [                  ]
                         [2    3    4    ...]

I don't understand your question. 

> simplify(5040^(1/7)/(z^7)^(1/7)) assuming z > 0;

5040^(1/7)/z

> simplify(5040^(1/7)/(z^7)^(1/7)) assuming z::complex;

5040^(1/7)/(z^7)^(1/7)

which is correct, because if z is complex Maple doesn't know which branch of (z^7)^(1/7) to use.

I don't understand your question. 

> simplify(5040^(1/7)/(z^7)^(1/7)) assuming z > 0;

5040^(1/7)/z

> simplify(5040^(1/7)/(z^7)^(1/7)) assuming z::complex;

5040^(1/7)/(z^7)^(1/7)

which is correct, because if z is complex Maple doesn't know which branch of (z^7)^(1/7) to use.

For 2-D input, you can use (from the main menu) menu Format, Convert To, 1-D Math Input, or right-click and from the context menu choose 2-D Math, Convert To, 1-D Math Input.  For output, you can either copy it to a 2-D math input area and proceed as above, or copy it to a 1-D math input area, or use the lprint command.  You could also go (from the main menu) to Tools, Options, Display, and change Output Display to Maple Notation, then click Apply to Session.  This will make all further output be in 1-D form until you change it back.

For 2-D input, you can use (from the main menu) menu Format, Convert To, 1-D Math Input, or right-click and from the context menu choose 2-D Math, Convert To, 1-D Math Input.  For output, you can either copy it to a 2-D math input area and proceed as above, or copy it to a 1-D math input area, or use the lprint command.  You could also go (from the main menu) to Tools, Options, Display, and change Output Display to Maple Notation, then click Apply to Session.  This will make all further output be in 1-D form until you change it back.

Don't knock it.  Without all this inefficient spending on unneeded gifts, the whole world economy would collapse.

You allow them to use mobile phones on exams?  How can you check that they are using the calculator function rather than texting to their friends?

Note that by Hall's Marriage Theorem, whenever no perfect matching exists there must be some set of gifters that is larger than its set of possible giftees.
The graph doesn't have to split into two components, though.

Yes, of course: only the Standard GUI supports typeset math in plots.

Yes, of course: only the Standard GUI supports typeset math in plots.