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

9^ (1/2b) : 3^a

27^ (1/3b) : 9^ (1/2a)

125^ (1/3a) : 25^ (1/2b)

1/27

1/27

125

Step-by-step explanation:

Given that,

a - b = 3

9^ (1/2b) / 3^a = 3^ (2/2b) / 3^a

= 3^b/3^a

= 3^ (b-a)

= 3^ (-3)

= 27^ (-1)

= 1/27

27^ (1/3b) / 9^ (1/2a) = 3^ (3/3b) / 3^ (2/2a)

= 3^b/3^a

= 3^ (b-a)

= 3^ (-3)

= 27^ (-1)

= 1/27

125^ (1/3a) / 25^ (1/2b) = 5^ (3/3a) / 5^ (2/2b)

= 5^a/5^b

= 5^ (a - b)

= 5^3

= 125