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Question

Show that there is no value of n for which (2n×5n) ends in 5.

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Solution

As per the equation an×bn=(ab)n

2n×5n=(2×5)n=10n

Any number multiplied by 10 always ends in 0. (The basic test of divisibility rule to check if a number is divisible by 10 is whether the final digit of the number is 0).


Thus, for any value of n, 10n will also end in 0. As a result, the value of 10n will never end with 5.


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