Math help needed

My daughter got a very challenging assignment.  She did wonderfully with about 80% of it, and then hit a wall.  I got intrigued and started helping her out, but I too have now hit a wall.  Perhaps you can help, because this is making me very frustrated.

Here’s the deal:  She was given the numbers 1, 2, 4 and 6.  Using addition, subtraction, multiplication and division, and using each of those numbers only once, she has to create mathematical statements that result in the numbers 1 through 50.

Here are some examples, all of which she figured out:

1 = 6+1-2+4

3 = 2+6-4-1

8 = [(6×1)+4]-2

39 = 62+4-1

44 = [(6×2)-1]x4

As you can see, not only is she using each of the assigned numbers only once, she can also use exponents.  Incidentally, you can create exponents, such as 5, by making the exponent 4+1.

Does that make sense? For those of you familiar with the old math game of Krypto, it’s like Krypto, only using four working digits, not five.

So, my daughter made fantastic progress, and I was able to help out with a few more.  We got completely stumped, though, trying to create formulas that would equal 34, 38 and 43.  Are those do-able or impossible?  I suspected some of you might know.