9th Grade Geometry Help?

Question

Hello, I'm doing math homework right now and i have stumbled on to this problem: What is the last digit of 2*85 (2 to the 85th power). Please help me, and explanations would be very much appreciated. Thank You.

Answer 1

You should use (shift + 6) for power of:

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

The pattern is 2, 4, 8, 6, 2, 4, 8, 6 etc...

On 2^84, the last digit is 6 because the it is a multiple of 4 which means it's the last one in the pattern. That means the next one must be 2 because the pattern starts over so 2^85 ends in 2.

Answer 2

powers of 2 (starting at 1) 2 , 4, 8 , 16, 32, 64, 128 , 256 ....

Notice how the last digit cycles  2,4,8,6,2,4,8,6 ..... repeating after every 4th power.

2^85 = 2^(21*4 + 1) = 2^(21*4) * 2^1

2 raised to any power which is a multiple of 4 gives a number ending in 6.  One more power of 2 then gives you something that ends in 2.

Answer 3

Haha

You go:

2 x 2 x 2 x 2 x .................2^85...  There is no easy way lady!

Sorry

And this problem just can't be a ninth grade problem

Answer 4

base 2 follows a pattern

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

2^6=64

2^7=128

2^8=256

as you can see the last digit alternates in the pattern 2,4,8,6,2,4,8,6 forever.

this pattern is a repeating unit of 4 digits in length so you see how many lots of 4 go evenly into 85. the answer is 21 lots although this part is unimportant. the remainder is 1 so the 85th power will have the same last digit as the first character.i.e the last digit will be a 2

hope that helped

Answer 5

2^85            [^ indicates to the power]

now

2^2=4

2^3=8

2^4=16

2^5=32

last digits are 4,8,6,2

2^6=64

2^7=128

2^8=256

2^9=512

last digits are 4,8,6,2

similarly every fourth power after 2^9 will have last digit as 2

i,e 2^13,2^17,2^21,2^25...2^49....

.....2^85 will have last digit as 2

Answer 6

the last digit is two, are you sure this is 9th grade geometry?

Answer 7

I get 38,685,626,227,668,100,000,000,000.

zero?

Feel free to double check my work.