Question

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

Answer 1

Answer:

$\dfrac{1}{27}$

Step-by-step explanation:

Given that,

a-b = 3

We need to find the value of $\dfrac{27^{\dfrac{1}{3}b}}{9^{\dfrac{1}{2}a}}$.

We know that,

$27=3^3\\\\9=3^2$

So,

$\dfrac{27^{\dfrac{1}{3}b}}{9^{\dfrac{1}{2}a}}=\dfrac{3^3^({\dfrac{1}{3}b})}{3^2^{\dfrac{1}{2}a}}\\\\=\dfrac{3^b}{3^a}$

We know that : $\dfrac{x^p}{x^q}=x^{p-q}$

So,

$\dfrac{3^b}{3^a}=3^{b-a}$

Since, b-a = -3. So,

$3^{b-a}=3^{-3}\\\\=\dfrac{1}{3^3}\\\\=\dfrac{1}{27}$

So, the value of the given expression is equal to $\dfrac{1}{27}$.