Question

A and b are positive integers and a–b = 3. Evaluate the following:
27/1/3 b/9/ 1/2 a

Answer 1

`(1)/(27)`

Explanation:

Given that,

a-b = 3

We need to find the value of
`\frac{27^{(1)/(3)b}}{9^{(1)/(2)a}}`.

We know that,

`27=3^3\\\\9=3^2`

So,

`\frac{27^{(1)/(3)b}}{9^{(1)/(2)a}}=\frac{3^3^({(1)/(3)b})}{3^2^{(1)/(2)a}}\\\\=(3^b)/(3^a)`

We know that :
`(x^p)/(x^q)=x^(p-q)`

So,

`(3^b)/(3^a)=3^(b-a)`

Since, b-a = -3. So,

`3^(b-a)=3^(-3)\\\\=(1)/(3^3)\\\\=(1)/(27)`

So, the value of the given expression is equal to
`(1)/(27)`.