If m, n are natural numbers, for what values of m, does 2n x 5n ends

1.	If m, n are natural numbers, for what values of m, does 2n x 5n ends in 5?
Answer» 2ⁿ x 5^m 2ⁿ is always even for all values of n. 5^m is always odd and ends with 5 for all values of m. But 2ⁿ x 5^m is always even and ends in 0. ∴ 2ⁿ x 5^m cannot end with the digit 5 for any values of m. No value of m will satisfy 2ⁿ x 5^m ends in 5.

If m, n are natural numbers, for what values of m, does 2n x 5n ends in 5?

Answer»

2ⁿ x 5^m

2ⁿ is always even for all values of n.

5^m is always odd and ends with 5 for all values of m.

But 2ⁿ x 5^m is always even and ends in 0.

∴ 2ⁿ x 5^m cannot end with the digit 5 for any values of m. No value of m will satisfy 2ⁿ x 5^m ends in 5.