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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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4 0
3 years ago
Read 2 more answers
I’m stuck can some one help me
abruzzese [7]

Answer:

3) Midpoint is (-4,0.5)

Option A is correct.

4) Midpoint is (2.5,0)

Option B is correct.

5) The factors are (x+4)(x-7)

Option C is correct.

6) The factors are (x+4)(x+2)

Option A is correct.

Step-by-step explanation:

Question 3

Find midpoint of the following:

(2,-7), (-10,8)

The formula used to find midpoint is: Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

We have x_1=2, y_1=-7, x_2=-10,y_2=8

Putting values and finding midpoint

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2-10}{2},\frac{-7+8}{2} )\\Midpoint=(\frac{-8}{2},\frac{1}{2} )\\Midpoint=(-4,0.5 )

So, Midpoint is (-4,0.5)

Option A is correct.

Question 4

Find midpoint of the following:

(2,-10), (3,10)

The formula used to find midpoint is: Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

We have x_1=2, y_1=-10, x_2=3,y_2=10

Putting values and finding midpoint

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\\Midpoint=(\frac{2+3}{2},\frac{-10+10}{2} )\\Midpoint=(\frac{5}{2},\frac{0}{2} )\\Midpoint=(2.5,0 )

So, Midpoint is (2.5,0)

Option B is correct.

Question 5

Factor each completely

x^2-3x-28

We will break the middle term and find factors

x^2-3x-28\\=x^2-7x+4x-28\\Taking\:common\\=x(x-7)+4(x-7)\\=(x+4)(x-7)

So, the factors are (x+4)(x-7)

Option C is correct.

Question 6

Factor each completely

x^2+6x+8

We will break the middle term and find factors

x^2+6x+8\\=x^2+4x+2x+8\\=x(x+4)+2(x+4)\\=(x+4)(x+2)

So, the factors are (x+4)(x+2)

Option A is correct.

7 0
3 years ago
Please help! <br><br> 6.2 divided by (2x + 1)= 2 1/3 divided by 4
guajiro [1.7K]

Answer:

x=2/3

Step-by-step explanation:

(2x+1)/2 = 2 1/3/4

Multiply 4 on both sides:

2x+1=2 1/3

Rewrite:

2x+1=7/3

Subtract 1 on both sides:

2x=4/3

Divide 2 on both sides:

x=2/3

Thus x=2/3

Hope this helps!

7 0
2 years ago
Read 2 more answers
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