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
Drupady [299]
3 years ago
15

What is the remainder when 3^99 is divided by 8?

Mathematics
2 answers:
yaroslaw [1]3 years ago
8 0
3^99 can be re-written as (4-1)^99
Let’s call 4 as x,and -1as y.

When we do the binomial expansion of (x+y)^99, and temporarily omit the coefficient, we obtain,
X^99+x^98*y+x^97*y^2+x^96*y^3.......x*y^98+y^99.

We know that 4 raised to any natural number grater than one,will divide 8 completely (4^2=16=8*2, and therefore every subsequent power of 4 can be rewritten in the form of 8k, where k is a natural number.)

The last two terms of this binomial expansion are,
(99 c 98) *x*y^98 + y^99.....(x C y represents x “choose” y)
99 C 98 is nothing but 99 ....... ( by using the n C r formula )
So the last two terms will be,
99*4*1+(-1)
=396-1=395
395 mod 8= (392 mod 8) + (3 mod 8) = 0+3=3
So our required answer has been obtained: 3

Hope that helps
Gnom [1K]3 years ago
3 0

Answer:

3

Step-by-step explanation:

3^1=3 divided by 8 will give a remainder of 3

3^2=9 divided by 8 will give a remainder of 1

3^3=27 divided by 8 will give a remainder of 3

3^4=81 divided by 8 will give a remainder of 1

3^5=243 divided by 8 will give a remainder of 3

You will notice that 3^n will give 3 when n is odd number and 1 when n is even number

Since n=99 and 99 is an odd number,

Then the remainder is 3

You might be interested in
Find the value of x.<br><br> HELP!!!! I WILL GIVE BRAINLIEST ANSWER!!! <br> POINTS!!!
STatiana [176]

Answer:

43

Step-by-step explanation:

its an isoceles triangle so both base angles are congruent

7 0
3 years ago
Does 2 feet and 1 inch add up too 3 feet
Makovka662 [10]

Answer:

No

Step-by-step explanation:

2 feet + 1 foot = 3 feet

1 foot = 12 inches, not 1 inch

If helpful, please give 5 star, thanks, and brainliest!

3 0
3 years ago
Read 2 more answers
Jayson used 0.5 cup of kernels to make 16 cups of popcorn. How many cups of popcorn would he make if he used 0.75 cup of kernels
notka56 [123]
Dividing both sides by 0.5

24 cups of popcorn can be made from 0.75 cups of kernels.
8 0
3 years ago
Write a <br> DEScription of bar graph
Karolina [17]
A bar graph is a chart that uses bars to show comparisons of different types of data. The bars can either be horizontal or vertical. They are always straight if I’m not mistaken
8 0
3 years ago
What value of x makes this equation true?
Flauer [41]

Answer:

27

Step-by-step explanation:

27/3-3=6 and 27/9+3=6

so both sides are equal to each other which makes the equation true.

7 0
3 years ago
Other questions:
  • 0.7 of what number is 4 1/2?​
    9·1 answer
  • Complete each blank to find an expression that is equal to 16%.
    10·1 answer
  • What is 2,767,545 to the nearest ten
    6·1 answer
  • Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. sec u = −2, π/2 &lt; u &lt; π
    7·1 answer
  • Which expression is equivalent to b^-e?<br>A. b+1/-e<br>B. 1/b^e<br>C. b^e
    5·2 answers
  • Jonathan has more than $20 in his piggy banks which of the amounts below could Jonathan have in his piggy bank $7.00 $31.00 $20.
    9·1 answer
  • A fish swins 12 miles upstream in 4 hours. The return trip only takes 3 hours. Find the rate of the current
    7·1 answer
  • PLEASE LOOK AT PICURE!!! I WILL MARM BRAINIEST TO WHOEVER IS CORRECT!!!
    6·2 answers
  • (y/x)¯10 ÷ (x/y)⁹ simplify​
    6·1 answer
  • How do you find x in the question \frac{x}{10}=0.1 how do you find out what x is???
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!