Question

Show that 5 power n cannot end with the digit zero,for any natural number n. Give reason also.

Answer 1

Let us assume to the contrary that 5^n can end with the digit 0

If any number ends with the digit 0, it should be divisible by 10

Hence 5^n=10k where k is a constant

5^n=2*5*k

This means that 2 & 5 are part of prime factorization of 5^n

But we observe that 2 is not a part of the prime factorization of 5^n

Hence our assumption is wrong

Hence 5^n can never end with the digit 0

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Answer 2

$\huge\bigstar$$\huge\bold\pink{Solution}\huge\bigstar$

The value of 5¹ = 5

The value of 5² = 25

The value of 5³ = 125______

The end value of 5^n is always 5 and it cannot be 0

$\huge\bold{Explanation:-}$

If a number say x^n should end with zero

It should be expressed in 5×2 prime factorisation

But 5 cannot be expressed in 5×2 terms

It can only be expressed in 5×1 factorisation

So, the end digit of 5^n cannot be zero