Prove that $5^{n} \times 6^{n}$ ends in zero for any natural number $n \in N$.

(N/A) To determine if $5^{n} \times 6^{n}$ ends in zero,we must check if it is divisible by $10$. $A$ number is divisible by $10$ if its prime factorization contains at least one pair of $2$ and $5$.
Given expression: $5^{n} \times 6^{n}$.
We can factorize $6^{n}$ as $(2 \times 3)^{n} = 2^{n} \times 3^{n}$.
Substituting this into the expression: $5^{n} \times 2^{n} \times 3^{n} = (2 \times 5)^{n} \times 3^{n} = 10^{n} \times 3^{n}$.
Since the expression can be written as $10^{n} \times 3^{n}$,it is clearly divisible by $10$ for all $n \in N$.
Therefore,$5^{n} \times 6^{n}$ always ends in zero for any natural number $n$.