Question

The unit digit of 3 to the power 34

Answer 1

Answer:

Here is your answer mate,

Step-by-step explanation:

Please check the attachment

Answer is 9

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Answer 2

Given: 3 to the power 34, i.e., $\[{3^{34}}\]$.

To find: The unit digit of the given number.

Solution:

Know that,

$\[\begin{array}{l}{3^1} = 3\\{3^2} = 9\\{3^3} = 27\\{3^4} = 81\\{3^5} = 243\end{array}\]$

Observe that, the units digit repeats after the index of 4.

Divide 4 by 34.

$\[\frac{{34}}{4} = 8\frac{2}{4}\]$

Therefore, the remainder remains 2 which means, $3^{2} =9$

Hence, the unit digit of 3 to the power 34 will be 9.