Answer:
[tex]xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
Step-by-step explanation:
Given expression,
[tex]\sqrt{x^2y^2}+2\sqrt{x^3y^4}+xy\sqrt{y}[/tex]
[tex]=(x^2y^2)^\frac{1}{2} + 2(x^3y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex]\because (\sqrt{x}=x^\frac{1}{2})[/tex]
[tex]=(x^2)^\frac{1}{2} (y^2)^\frac{1}{2} + 2(x^3)^\frac{1}{2} (y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex](\because (ab)^n=a^n b^n)[/tex]
[tex]=x^{2\times \frac{1}{2}} y^{2\times \frac{1}{2}} + 2(x^{3\times \frac{1}{2}})(y^{4\times \frac{1}{2}})+xy\sqrt{y}[/tex]
[tex]\because (a^n)^m=a^{mn}[/tex]
[tex]=x^1 y^1 + 2x^{1\frac{1}{2}} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2x.(x)^\frac{1}{2} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2xy^2\sqrt{x}+xy\sqrt{y}[/tex]
[tex]=xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
