what is the units digit of the number 373 power 333. explain with steps

Dear Student,

Please find below the solution to the asked query:

Unit digit of ( 373 )³³³  is depend on the power of unit digit of  373 , So

3³³³ gives same unit digits as ( 373 )³³³ 

And we know :

3¹ = 3 ,

3² = 9 ,

3³ = 27 ,

3⁴ = 81 ,

3⁵ = 243

Here we can see that ,  The pattern repeats every four digits.

And 

$\frac{333}{4} = \mathbf{83}\frac{\mathbf{1}}{\mathbf{4}}$  , 1 is remainder and pattern repeat itself by 83 times and then ( We know 3¹ = 3 ) 

So ,  Unit digit of 3³³³ is " 3 " 

Therefore,

Unit digit of ( 373 )³³³   = 3                                                                     ( Ans )


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