Question

Find the unit digit of (23)^148​

Answer 1

Answer:

3¹ =3

3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

i.e unit digit repeat after 4 power so it's cyclicity is 4.

now (23)¹⁴⁸ = ((23)⁴)³⁷ = (unit digit of 23⁴ = 1)³⁷ = 1

Ans.

Answer 2

Answer:

Unit place of $23^{148} = 1$

Step-by-step explanation:

The way of solving this kind of question is that we have to find a sequence of the digit of unit place by multiplying to accending order their powe. And after some multiplication we get a repeation of unit place digit.

In the question $(23)^{148}$.

Unit place is 3.

So,

$3^{1} = 3\\3^{2}=9 \\ 3^{3}=27 \\3^{4}=81\\ 3^{5}=243\\ 3^{6}=729$

Here after 4th power the unit place is repeat again.

so, 148/4 = 37 + 0.

It means it is completely divided by 4 and the unit digit is the digit of $3^{4} = 81$ which is 1.

THANKS.

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