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My name is Ann [436]
3 years ago
10

What is the last digit of 3^36th power? Please explain, I still do not understand why it is 0.

Mathematics
2 answers:
Dafna11 [192]3 years ago
3 0

The answer is actually 1, and not 0, and here's why.

Write 3^36 into (3^3)^12. Note that the exponents 3 and 12 multiply to 36

Now focus on 3^3 which turns into 27. The last digit here is 7. It turns out that this is the only thing that matters when it comes to finding the final answer.

So instead of 27^12, we can look at 7^12

Break 7^12 into (7^3)^4, then note how 7^3 = 343. Again the units digit is all we care about. So instead of 343^4, we just look at 3^4

3^4 = 81 and the units digit here is 1 which is the final answer.

---------------------------------

Here's an alternative approach using modular arithmetic. This is the set of tools that helps us find remainders. If we work with mod 10, then we can find the units digit of any complicated expression such as 3^36

3^36 = (3^3)^12   (mod 10)

3^36 = 27^12 (mod 10)

3^36 = 7^12 (mod 10)

3^36 = (7^3)^4 (mod 10)

3^36 = 343^4 (mod 10)

3^36 = 3^4 (mod 10)

3^36 = 81 (mod 10)

3^36 = 1 (mod 10)

We effectively follow the same steps as mentioned above, but we're using a more formal set of steps to show.

Schach [20]3 years ago
3 0

Answer:

  The last digit is 1.

Step-by-step explanation:

3^36 = 150094635296999121

The last digit is 1.

The digit cannot be zero because there are no factors of 10 in 3^36.

_____

Consider the last digits of powers of 3:

  3^0 = 1

  3^1 = 3

  3^2 = 9

  3^3 mod 10 = 7

  3^4 mod 10 = 3·7 mod 10 = 1

The last digit repeats in the pattern 1, 3, 9, 7, 1. So every 4th exponent will have the same result.

So, 3^36 mod 10 = 3^(36 mod 4) = 3^0 = 1.

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3 0
3 years ago
A farmer wants to enclose a rectangular field that borders a river with 400 feet of fencing material. if the farmer does not fen
ICE Princess25 [194]
Let each side perpendicular to the river be "x".Then the side parallel to the river is "400-2x".
The formula for Area = width*length
A(x) = x(400-2x)
A(x) = 400x - 2x^2
You have a quadratic with a = -2 and b = 400
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3 0
3 years ago
Jackie earns $172 per week at her part time job. She is saving this money to buy a used car that cost $2000. At this rate, how m
vodomira [7]

Answer:

12 weeks

Step-by-step explanation:

It will take Jackie 12 weeks to buy her car because she earns 172 per week.

If you divide 2000 buy 172 you end up with 11.6

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Hope this helps.

3 0
2 years ago
Simplify, using the distributive property and then combining like terms. 2(x+y)+(2x−2y)
Tamiku [17]

Answer:

4x

Step-by-step explanation:

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