Answer:
[tex]\dfrac{1}{27}[/tex]
Step-by-step explanation:
Given that,
a-b = 3
We need to find the value of [tex]\dfrac{27^{\dfrac{1}{3}b}}{9^{\dfrac{1}{2}a}}[/tex].
We know that,
[tex]27=3^3\\\\9=3^2[/tex]
So,
[tex]\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}[/tex]
We know that : [tex]\dfrac{x^p}{x^q}=x^{p-q}[/tex]
So,
[tex]\dfrac{3^b}{3^a}=3^{b-a}[/tex]
Since, b-a = -3. So,
[tex]3^{b-a}=3^{-3}\\\\=\dfrac{1}{3^3}\\\\=\dfrac{1}{27}[/tex]
So, the value of the given expression is equal to [tex]\dfrac{1}{27}[/tex].
