Answer: [tex]\frac{4^{0.5 a}}{2^{b}}=4[/tex]
Step-by-step explanation:
We are told [tex]a-b=2[/tex] being [tex]a[/tex] and [tex]b[/tex] positive integers, hence:
[tex]a=2+b[/tex] (1)
Now we have the following expression:
[tex]\frac{4^{0.5 a}}{2^{b}}[/tex] (2)
Which can be also written as:
[tex]\frac{2^{2(0.5 a)}}{2^{b}}[/tex] (3)
Since [tex]4=2^{2}[/tex]
Then, substituting (1) in (3):
[tex]\frac{2^{2(0.5(2+b))}}{2^{b}}[/tex] (4)
Since we have exponents with the same base, we can do the following:
[tex]\frac{2^{2+b}}{2^{b}}=2^{2+b} 2^{-b}[/tex] (5)
Finally:
[tex]2^{2+b} 2^{-b}=2^{2+b-b}=2^{2}=4[/tex] (6)
Hence:
[tex]\frac{4^{0.5 a}}{2^{b}}=4[/tex]
