Question

What is The number In the units place of (763)⁸⁴?

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Answer 1

Required Answer:-

The unit digits of certain numbers repeats after definite interval and this is known as cyclicity. Here the unit of the base number is 3.

In case of 3,

• 3¹ = 3
• 3² = 9
• 3³ = 27
• 3⁴ = 81
• 3⁵ = 343 (repetition and so on...)

The units digit repeat at a interval of 4. So, if we divide the power of the base number by 4, the remainder will determine the unit digit of the number.

1. If remainder is 1, unit digit is 3
2. If remainder is 2, unit digit is 9
3. If remainder is 3, unit digit is 7
4. If remainder is 4/0, unit digit is 1.

Since we are dividing the power by 4, the remainders can only be 1,2,3 or 0.

Given:-

$\boxed{ {763}^{84} }$

Power is 84. If 84 is divided by 4, the remainder is 0. Hence the unit digit of the number is 1 (ans).

Answer 2

Answer:

1

Step-by-step explanation:

Since we need to find only unit digit of (763)^84

We will find (3)^84 because 3 is at unit digit of 763

(3)^84 can be written as ((3^4))^21

=> (81)^21

Now we will find (1)^21 because 1 is at unit digit of 81

=> (1)^21

=> 1 Answer