Respuesta :
a^2 * b^3 = 108 this is true for a = 2 and b = 3. So 2a + 3b = 2(2) + 3(3) = 4 + 9 = 13
The values of the positive intergers a and b is 2 and 3 respectively and the value of 2a+3b is 13.
What is algebraic expression?
Algebraic expression are the expression which consist the variables, coefficients of variables and constants.
In the given problem, a and b are positive integers. The given expression in the problem is,
[tex]a^2b^3=108[/tex]
Let us the hit and trial method to make both the equation equal. For a=1 and b= 1 the expression will be equal to 1. For a =2 and b=3,
[tex](2)^2(3)^3=108\\(4)(27)=108\\108=108[/tex]
Here, left hand side of the expression is equal to the right hand side of the expression for a =2 and b=3. Thus the value of a and b are,
[tex]a=2\\b=3[/tex]
The value of the expression we have to find is,
[tex]2a+3b[/tex]
Put the values of a and b in the above expression, we get,
[tex]2a+3b=2(2)+3(3)\\2a+3b=4+9\\2a+3b=13[/tex]
Hence, the values of the positive intergers a and b is 2 and 3 respectively and the value of 2a+3b is 13.
Learn more about the algebraic expression here;
https://brainly.com/question/2164351
