Simplify - Challenge Question

When we are coding, the computer always interprets commands 100% literally. Therefore, it only knows what we tell it. If someone wrote sin(2π n), we would probably assume that they meant that n was an integer and that sin(2π n) reduced to zero. However, Mathematica will not do this. Therefore, we need to always be careful to specify every condition that we want Mathematica to assume.

1 a) A student has written the following code. Why does ((((x^(2 ))))^0.5)not simplify to x?

Simplify[((((x^2)))^0.5)]

b) Add in an assumption so that Mathematica will simplify the command to x. What would that assumption need to be?

2a) Use simplify to evaluate ((((x^4)))^(1/2)), (without any additional assumptions about the value of x).

b) Suggest a value of x, such that (x^2)≠((((x^4)))^(1/2)) .

c) Without specifying that x>0, write a condition such that ((((x^4)))^(1/2)) simplifies to (x^2).