1. The problem statement, all variables and given/known data φ is a homomorphism of groups. φ: ℝ^x -> ℝ^x, where φ(α) = α^4, for all α ∈ ℝ^x. Note that ℝ^x is a group under multiplication. Describe ker(φ) and Im(φ). 2. Relevant equations 3. The attempt at a solution This is another one of those problems that has me scratching my head due to the way it is written. What does ℝ^x mean? A real number exponentiated? If all it does is take α and map it to α^4, then the kernal is just going to be the same as it would be without the mapping? The image is just exponentiated 4 times. er?