1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Please don't give me a link as an answer
tino4ka555 [31]

Answer:

x=2

Step-by-step explanation:

x+2=4

x=2

6 0
3 years ago
Read 2 more answers
In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, th
earnstyle [38]

Answer:

Step-by-step explanation:

new length=15+x

width=19+x

then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²

original area=15×19=285 ft²

then 285+98=x²+34x+285

or

x²+34x-98=0

x²+34x+17²=98+17²

(x+17)²=98+289=387

x+17=√387=3√43

x=3√43-17 ft

8 0
3 years ago
Put the following equation of a line into slope-intercept form, simplifying all
lisabon 2012 [21]

Answer:

y = -5x-9

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

10x + 2y = -18

Subtract 10x from each side

10x + 2y-10x =-10x -18

2y = -10x-18

Divide each side by 2

2y/2 = -10x/2 -18/2

y = -5x-9

8 0
3 years ago
If the point (x,/3/3) is on the unit circle what is x
Firlakuza [10]
The answer is B.

I  hope this helps. :)
6 0
3 years ago
While playing volleyball, Ralph drink 3/4 of a jug of water. If the jughead 64 fluid ounces of water, how many fluid ounces of w
MaRussiya [10]

Answer:

48

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • The scale model of a skyscraper being built is 4.2 feet tall. When it is finished, the skyscraper will be 525 meters tall. What
    12·1 answer
  • Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that cont
    9·1 answer
  • Sum of two numbers is 20 their difference is 118
    15·1 answer
  • Find the length of the midsegment.
    14·1 answer
  • HELP ME PLEASE ASAP!!!!!!!!
    10·1 answer
  • What is the solution to -18 + k = 37 A. k = 55 B. k = 19 C. k = -19 D. k = -55
    9·2 answers
  • 1/5 k = 20 solvve for k
    5·2 answers
  • PNC Bank gives 0.5% interest on their savings accounts. An account has a balance of $1,500. What will the total balance be after
    11·1 answer
  • Sara has 37 bugs in her collection she will collect 8 new bugs bevery day. Sara will collect bug for times days for what value o
    8·1 answer
  • for a basic subscription, a cable television provider chargers and activation fee of $60, plus $125 per month. what linear funct
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!