If $n$ is any natural number, then $9^{n} - 5^{n}$ may end with ___________.

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Solution

The correct option is B 6
$9^{1} = 9$
$9^{2} = 81$
$9^{3} = 729$
$9^{4} = 6561$
$∴$ On generalising, $9^{n}$ ends with either 9 or 1.
Similarly, $5^{n}$ ends with only $5$ .

When $9^{n}$ ends with 9, then $9^{n} - 5^{n}$ ends with 4 as 9 - 5 = 4.
When $9^{n}$ ends with 1, then $9^{n} - 5^{n}$ ends with 6.

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