Question

A and b are positive integers and a−b=2. Evaluate the following: 4^0.5a/ 2^b

Answer 1

4

Explanation:

Answer 2

Answer:
`(4^(0.5 a))/(2^(b))=4`

Explanation:

We are told
`a-b=2` being
`a` and
`b` positive integers, hence:

`a=2+b` (1)

Now we have the following expression:

`(4^(0.5 a))/(2^(b))` (2)

Which can be also written as:

`(2^(2(0.5 a)))/(2^(b))` (3)

Since
`4=2^(2)`

Then, substituting (1) in (3):

`(2^(2(0.5(2+b))))/(2^(b))` (4)

Since we have exponents with the same base, we can do the following:

`(2^(2+b))/(2^(b))=2^(2+b) 2^(-b)` (5)

Finally:

`2^(2+b) 2^(-b)=2^(2+b-b)=2^(2)=4` (6)

Hence:

`(4^(0.5 a))/(2^(b))=4`