At the beginning of class, students were given what was last year's quiz I gave after teaching and practicing some exponent rules. The instructions:
1) Answer every question with your best guess. We haven't learned this stuff yet, so I don't expect you to get many of the questions right, but I do want you to try to make some sort of guess for each.
2) Use your laptop to go to wolfram alpha to check each of your answers. Write the correct answer separate from your original answer and try to figure out what each exponent rule is.
3) For each answer you got wrong originally, make up 3 similar problems that use the same rule(s), answer them and check them using Wolfram Alpha.
4) Once you are confident that you could get every problem right without help, I will give you your quiz.
The result? Students did better on the quiz than in previous years where I taught the material. Granted, there are some other variables involved in that, but it was clear from moving around and talking to them that figuring out the rules themselves gave them a better understanding of what was going on. The whole thing took two 45 minute periods, part of which was getting them used to typing the expressions and a discussion about why they shouldn't use wolfram alpha to do all of their homework for them.
You may be saying to yourself "Hey wait a minute, you could've just given them an answer sheet and done the same thing." Well yes, and no. Answer sheets would take away the flexibility of being able to check answers to the problems that they make up. The making up step also helps them to understand what they are really looking for and is a good strategy they can use to help study for tests. Also, part of the point(which I discussed with them) was to get them used to using Wolfram alpha to check their work any time, like for homework or studying for instant feedback.
Now as pleased as I am with how this went I'm certainly not ready to give up explaining things at the board ever. Exponent rules lend themselves well to this sort of activity as they are reasonable to figure out with the answers and I'm definitely going to look for more topics that would work well with this kind of activity in the future. Can you think of any?