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
What is the range of this function?
Lostsunrise [7]

Answer:

c \: is \: correct \:  \:  \: the \: range \: is \: usually \: right \ \\ : and \: they \: are \: x \:

5 0
3 years ago
Please answer fast!!!!!
BlackZzzverrR [31]

Answer:

x = 2

Step-by-step explanation:

note that 4096 = 8^{4} , then

8^{2x} = 8^{4}

Since bases on both sides are equal, both 8 , then equate the exponents

2x = 4 ( divide both sides by 2 )

x = 2

6 0
3 years ago
Read 2 more answers
Don,Eric, and Finn line up in random order for the cafeteria line. What is the probability that they will line up from front to
Vanyuwa [196]

Answer:

  1/6

Step-by-step explanation:

The number of ways they can line up is 3×2×1 = 6. Only one of these is alphabetical order. The probability that they will line up randomly in alphabetical order is 1/6.

__

Any of the three can line up first; either of the remaining two can line up second, and the remaining person can line up last. Thus there are 3×2×1 possible orders.

5 0
3 years ago
Read 2 more answers
What is the slope of a line that passes through the points (-4,0) and (0,4)?
Schach [20]

Answer:

1

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Ricardo has a spinner and a bag of marbles filled with 2 red marbles, 3 green marbles, and 3 blue marbles. What is the probabili
Alexandra [31]
1/16!!!!!!!!!! Is the correct
8 0
2 years ago
Other questions:
  • How many significant digits are in the number 8.1000?
    14·2 answers
  • What are the answers to this and please explain briefly
    10·2 answers
  • 7. The pair of polygons is similar. Find the value of x.
    14·1 answer
  • A brand new filled jar of salsa is 11 cm tall and a has a radius of 6 cm. Kelly eats some of the salsa and the salsa in the jar
    10·1 answer
  • The x- and y-coordinates of the focus of a parabola are (1,3) and the directrix is y=-5 . A second parabola is a translation 1 u
    5·1 answer
  • What is the area of the parallelogram given?
    9·2 answers
  • Hello pls help me with two of these questions;)
    5·1 answer
  • The Length of a rectangle is 3 meters more than the width. The perimeter of the rectangle is 26 meters. if the width is B which
    7·2 answers
  • Emily, Zeke, Harry, and Brook each conducted surveys on the number of books people have in their homes. Then, each student deter
    6·2 answers
  • Pls help need asap in 10 mins
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!