Unusual Equations (Index Laws)

You can use this in a number of ways.

I sometimes get the kids to solve by trial and error (good practice for substitution on a calculator). When they get an x that "works" I write it up on the board. With a board full of solutions I then ask them if they can find any patterns.

Alternatively you could insist that they use index laws to solve the equations in the first place.

Opportunities to discuss 1^n=1, n^0=1, (-1)^2n=1 and 0^0=undefined.