Varied names around the world for the same topic! (NB> New Aus. Curriculum is moving to exponents!)
A key starting point in looking at this though is probably Michael Fenton’s blog on the topic, in particular noting the way he talks about the indices as ‘number of factors of’. This idea is talked about further here on Sara’s site where she also includes some other ideas worth looking at. I found the factors idea particularly helpful when discussing fractional indices (it was one of three ways I looked at it – the other of the two ways I think students found helpful was just recognising, for example, how 9^1/2 x 9^1/2 = 9, therefore 9^1/2 must be 3).
In 2021 I came across this desmos activity on square and square root – the task is ok (card sort too crowded), but I particularly liked the simplicity/clarity of ideas around the square visual on the video included on the 2nd slide.
NB. Robert Kaplinsky’s ‘Depth of Knowledge‘ page includes a sample of ideas relating to indices (as well as fractions and equations)
This seemed like a good desmos activity – described as combining desmos with open middle!
Don’t know where I came across this ‘flippity scavenger hunt‘?!? but was fun working through the locks – didn’t do them all but seem to be good indice questions/solving equations etc.