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A cheap cleaner for battery connections is baking soda and water; you can use this with a wire brush to remove corrosion.
There are also chemical sprays made specifically for dissolving corrosion, available at any auto parts store for less than $4.
To protest against future corrosion, there are various methods. You can buy chemically treated felt washers to put under the battery clamps. THere are also specific battery terminal spray coatings available at auto stores for this purpose.
In the old days, mechanics used axle grease to coat the terminals. I prefer a clear spray shellac; as it is less messy. The idea is to keep the air off of the bare metal, as oxygen is essential for the corrosion process to take place.
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