• $2^{30}-2^{20}=2^{10}$ (answer given by three six different students [a whiff of plagiarism?], but I can see where they were coming from; in any case the result is undeniably correct)
• $2^{30}-2^{20}=x$, $2^{10}=x$ (refinement on the theme above, with a more algebraic flavour)
• $\frac{2^{30}}{2^{20}}=2^{18}$ (also correct, to a factor of $256$)
• $2^{30} \div 2^{20}=2^{1.5}$ (wait, the previous result has now been challenged...)
• $\frac{2^{20}}{2^{30}}=2^{50}$ (intriguing... from the above one would have inferred $2^{-18}$ or $2^{-1.5}$...)

• $\frac{2^{32}}{2^{20}}=12$ (the deeper reasons for this result are clear, but they are also vertigo-inducing)
• $2^{12}\times 2^{10}=2^{120}$ (an astronomical finding, somehow connected to $2^{1.5}$ above)
• $2^{30}=\frac{32}{2^{20}}$ (judging from the previous computation, this is a gross underestimation)

Update (2022): the power struggle rages on

• $\frac{30}{20}=10 \to 10$ bytes (refreshing innovation)
• $\frac{2^{30}}{2^{20}}=2^{50}$ (augmentation strategy)
• $\frac{2^{20}}{2^{30}}=2^{10}$ (nearly there...)

Now, you should agree with me that some students need some empowering (even if the above corresponds to less than 10% of the class).