Question

For what value of n, 2ⁿ × 5ⁿ ends in 5.

Answer 1

We need to find the value of n, for which  `2^nxx5^n` ends in 5.

Clearly, 

`2^nxx5^n = (2xx5)^n`

`= 10^n`

Also, all the values of n will make `10^n` end in 0.

Thus, there is no value of n for which `2^nxx5^n ` ends in 5.