The value of the expression such that a and b are integers is 1/9
Indices and exponents
An exponential function is a mathematical function in the form y = ab^x
Given the indices expression
[tex]\frac{(9\frac{1}{2} )^b}{3^a}[/tex]
This can be simplified as:
[tex]=\frac{(3^{2*\frac{1}{2}} )^b}{3^a}\\=\frac{3^b}{3^a}[/tex]
According to the law of indices, the expression will becomes;
[tex]\frac{3^b}{3^a} =3^{b-a}[/tex]
Recall that a - b = 2, such that b - a = -2. Substitute into the result to have:
[tex]\frac{3^b}{3^a} =3^{b-a}\\3^{b-a}=3^{-2}\\3^{b-a}=1/9[/tex]
Hence the value of the expression such that a and b are integers is 1/9
Learn more on indices here: https://brainly.com/question/10339517
