Question

For what value of n, $2^{n}*5^{n}$ ends in 5.

Answer 1

SOLUTION :  

Given : 2ⁿ × 5ⁿ

If n = 1 , then 2 × 5 = 10

If n= 2 , then 2² × 5² = (2 × 5)² = 10² = 100 and so on.

Thus, for any value of n , we get that 2ⁿ × 5ⁿ ends with zero (always ) .

Hence,  for no value of n, 2ⁿ × 5ⁿ ends with 5.

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Answer 2

2^n×5^n is a number with factors that are multiples of 5,2.

5^n always ends with 5.
And 2^n always end s with 4,8,6,2 only .

So, 5×(4×8×6×2) will always end at 0.

Hence n do not exist at all.

Exp...
If n=0 then value is20×50=1×1=1


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