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Explanation:
Here, you just need to look at the oxidation state of the Mn atom.
In KMnO4 - the Mn is +7.
If you put it in an acidic medium, you get this:
MnO4¯ + 8H+ + 5e- → Mn2+ + 4H2O
As you can see, Mn gives up 5 electrons. (Making it an oxidizing agent.)
In a strongly alkaline solution, you get:
MnO4¯ + e- → MnO42-
So, it only gives up one of it's electrons. Making it a much weaker oxidizing agent.
(In a neutral solution, it gives up 3 electrons to form MnO2 and some hydroxide ions.)
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