Answer:
The simplified given expression [tex]\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}[/tex] is [tex]5x^3y^3[/tex]
Step-by-step explanation:
Given expression is
[tex]\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}[/tex]
To find the simplified expression:
[tex]\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=\frac{3x^2.x^-1}{2y^1}.\frac{10x^2y.y^3}{3}[/tex] ( Using the properties [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] and [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\frac{3x^{2-1}}{2y}.\frac{10x^2y^{1+3}}{3}[/tex]
[tex]=\frac{3x}{2y}.\frac{10x^2y^4}{3}[/tex] (using division property to the terms)
[tex]=5x^{1+2}y^{4-1}[/tex] ( Using the properties [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] and [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=5x^3y^3[/tex]
Therefore [tex]\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=5x^3y^3[/tex]
Therefore the simplified given expression is [tex]5x^3y^3[/tex]
Therefore simplified expression is given by [tex]\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=5x^3y^3[/tex]
