Doubly Powerful

To what power should $4^4$ be raised to give $8^8$?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


To what power should we raise $4^4$ to get $8^8$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.