Question

What is the unit’s digit in the number got from the following operation: (23)10

Answer 1

when any number is multiplied by 10 then it's unit place is 0
unit place of( 23)10is 0

Answer 2

Answer:

The unit's digit of the mentioned operation is 9.

Step-by-step explanation:

The given operation is (23)^10 or we can write $(23)^{10}$

• The unit digit in  $(23)^{10}$ = The unit digit in $3^{10}$
• Finding unit digit in $3^{10}$ : We can break  $3^{10}$ as following:

           $3^{10}$ = $3^{2 \times 5}$ = $(3^2)^5$ = 3² × 3² × 3² × 3² × 3²

                                      = 9 × 9 × 9 × 9 × 9

                                      = 81 × 9 × 9 × 9

                                      = 729 × 9 × 9

                                      = 6561 × 9 = 59049

 Here in 59049 the digit in unit's place is 9.

  ∴ In $3^{10}$ the unit place digit is 9.

• As, The unit digit in  $(23)^{10}$ = The unit digit in $3^{10}$

       so, The unit digit in  $(23)^{10}$ = 9.

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