I was trying to find these powers, but to my disappointment I only found $2^4 = 4^2$. Edit: $a$ must be different to $b$ of course.
Is that the only possible setting, and why? If we assume the number and the power can have also decimal values.
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a=b will work forever – Dominic Michaelis Apr 08 '13 at 19:07
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You mean other than a = b? – user541686 Apr 08 '13 at 19:08
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@Aryabhata, my math is a bit rusty, does that explain the x and y must be integers in order that to work? I am looking for decimal solutions too. – mathnewbie Apr 08 '13 at 19:12
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@mathnewbie: The answers generalize them... – Aryabhata Apr 08 '13 at 19:15