A and b are positive integers and a-b=2. Evaluate the following: 3^b/3^a

The answer is 1/9.

Step-by-step explanation:

Using the equation a-b=2, we can solve that a = 2+b.

We can then substitute that into the expression given to get 3^b/3^ (2+b).

Since they have the same base, we can subtract the exponents from the numerator and denominator to get 3^ (b-2-b) which simplifies to 3^-2.

3^-2 is simply 1/9.

using laws of exponents ...

m^a/m^b = m^a-b

therefore,

3^b/3^a = 3^b-a

=> 3^-2/

=> 1/3^2

=> 1/9