Question

2^a/2^b = 512
What is a - b?

Answer 1

a - b = 9

Explanation:

using the rule of exponents

`(a^(m) )/(a^(n) )` =
`a^(m-n)` , then

`(2^(a) )/(2^(b) )` =
`2^(a-b)` , so

`2^(a-b)` = 512 =
`2^(9)`

since bases on both sides are equal, both 2 then equate exponents

a - b = 9

Answer 2

a - b = 9

steps and explanation:

• 
  `(2^a)/(2^b) = 512`

• 
  `2^(a - b ) =512`

• 
  `2^(a - b ) = 2^9`

• 
  `a - b = 9`