Question

Show that there is no value of n for which ($2^n\times 5^n$) ends in 5.

Answer 1

As per the equation $a^n\times b^n=(ab{)}^n$

$2^n\times 5^n=(2\times 5{)}^n={10}^n$

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, ${10}^n$ will also end in 0. As a result, the value of ${10}^n$ will never end with 5.