Answer:
-12
Step-by-step explanation:
The given expression is
[tex]x^{-\frac{3}{2}}y\sqrt{36xy^2}[/tex]
We have to rewrite the given function in the form of
[tex]ax^{b}y^c[/tex] ....(i)
then we have to find the product of a,b and c.
The given expression can be rewritten as
[tex]x^{-\frac{3}{2}}y\sqrt{36}\sqrt{x}\sqrt{y^2}[/tex]
Using properties of exponents we get
[tex]x^{-\frac{3}{2}}y6x^{\frac{1}{2}}y[/tex] [tex][\because \sqrt[n]{a}=a^{\frac{1}{n}}][/tex]
[tex]6x^{-\frac{3}{2}+\frac{1}{2}}y^{1+1}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]6x^{-1}y^{2}[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=6,b=-1,c=2[/tex]
Product of a,b and c is
[tex]abc=(6)(-1)(2)=-12[/tex]
Therefore, the product of a,b, and c is -12.
