Question

show that 4n is never ending with zero​

Answer 1

Answer:

Step-by-step explanation:

4n= (2*2)n

now, we know that for the any number to end with 0, its prime factorisation must contain 5.

by the uniqueness of fundamental theorem of arithematic, the prime factorisation of 4n will always be equal to (2*2)n.

therefore, 4n can never end with the digit zero for an real number n

Answer 2

Step-by-step explanation:

→ No, 4ⁿ can never end with the digit 0 for any natural number n .

→ If 4ⁿ ends with 0 then it must have 5 as a factor .

But, 4ⁿ = ( 2² )ⁿ = 2²ⁿ .

→ It shows that 2 is the only prime factor of 4ⁿ .

Also, we know from the fundamental theorem of airthematic that the prime factorisation of each number is unique .

So, 5 is not a factor of 4ⁿ .

Hence, 4ⁿ can never end with the digit 0 .