## Monday, 11 August 2008

### Interesting Last Digit Of Exponent Value

Maths reveals its beauty in many ways.

Here, I like to explain about a special property of exponent (or power) to certain integer.

This know-how will come in useful when we are checking for correctness in the last digit of the answer when we do integer exponential.

Here it goes ....

(The last digit I shall be talking about is the one's unit of the integer.)

When we perform powering of even integer, the last digit of the answer is always even.
24 = 16
25 = 32
63 = 216

When we power integer ending with 5, we get the last digit of the answer also with 5.
52 = 25
15 3 = 3375

When we power integer ending with 6, we get the last digit of the answer also with 6.
62 = 36
16 3 = 4096

When we do integer to the power of 5, we get the last digit of the answer with number same as the last digit of the original integer.
25 = 32
65 = 7776
135 = 371293

This property of the last digit, after performing exponent to integer, helps us not only in checking for correctness of the last digit, but also make us realise that maths has its own set of exciting and beautiful characteristics for some mathematically operations applied to some numbers.

Maths stands out in this sense as compared to other subjects.
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