2^3/2^8=? Am I correct?

Question

My answer should be in the form of 2 raised to a power. im not entierly sure of my answer. Can someone verify? 

 

Related question:

what about fractions? For example my paper says, 1/16. and my answer should be in the form of 2 raised to a power. How do I solve that aswell?

Answer 1

Well, there is:
(2*2*2) / (2*2*2*2*2*2*2*2)
1 / (2*2*2*2*2)
1 / 2⁵
2^-5

Also --
1 / 16
1 / (2*2*2*2)
1 / 2⁴
2^-4

This is because, be definition, x^-n = 1/xⁿ

Answer 2

Two ways possible:

 

2³ / 2⁸

8 / 256

1 / 32

 

2³ / 2⁸

2^3-8

2^-5

1 / 2⁵

1 / 32

Answer 3

when you divide and the bases are the same you subtract the bottom exponent from the top exponent

2^3/2^8=2^(3-8)

2^(3-8)=2^(-5) is the answer

and also 2^(-5)=1/(2^[5])=1/32, not 1/16

doing it the long way...

2^3=8

2^8=256

8/256=4/128=2/64=1/32 or simply divide both terms by 8 to get 1/32