If the last digit pattern of 11, 12 and 13 are 1, 2, and 3, what does this mean about any whole number taken to a power?

Expert Answers

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It means that the last digit of the power of the whole number will be the same as the last digit of the power of its last digit.

 

Why?

Let's write 11=10+1

12=10+2,

13=10+3 ,

23=2*10+3 and

any number`??????a=10x+a`

where `a ` is the last digit .


Look at `(??????a)^n=(a+10x)^n=a^n+n*10*a^(n-1)x+n(n-1)/2a^(n-2)100x^2+.....`

The first term of the sum is `a^n `. Any other term of the sum will contain a power of 10. Therefore the last digit of any other term of the sum is 0

`(?????a)^n=a^n+10("something")`

The last digit of a power of the whole number will be the last digit of the power of `a` .

 

 

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