Question

Simplify the expression

Answer 1

Answer:

The simplified given expression $\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}$ is $5x^3y^3$

Step-by-step explanation:

Given expression is

$\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}$

To find the simplified expression:

$\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=\frac{3x^2.x^-1}{2y^1}.\frac{10x^2y.y^3}{3}$   ( Using the properties $\frac{a^m}{a^n}=a^{m-n}$ and   $a^m.a^n=a^{m+n}$ )

$=\frac{3x^{2-1}}{2y}.\frac{10x^2y^{1+3}}{3}$

$=\frac{3x}{2y}.\frac{10x^2y^4}{3}$ (using division property to the terms)

$=5x^{1+2}y^{4-1}$  ( Using the properties $\frac{a^m}{a^n}=a^{m-n}$ and  $a^m.a^n=a^{m+n}$ )

$=5x^3y^3$

Therefore $\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=5x^3y^3$

Therefore the simplified given expression is $5x^3y^3$

Therefore simplified expression is given by $\frac{3x^2y^{-1}}{2x}.\frac{10x^2y}{3y^{-3}}=5x^3y^3$