Question

Find each product or quotient.

$\frac{6x^2{y}^4}{12}\cdot \frac{3x^3{y}^2}{xy}$

Short answer

The final product of the expression is $\frac{3x^4{y}^5}{2}$.

Step-by-step solution

Step 1. Define the concept.

Multiplying rational expression: - Let a, b, c, and d be polynomials with$b\ne 0$ and $d\ne 0$. Then .$\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$

Dividing rational expression: - Let a, b, c, and d be polynomials with $b\ne 0$,role="math" localid="1648047585675" $c\ne 0$ and $d\ne 0$. Then $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}=\frac{ad}{bc}$.

Step 2. Divide by the common factors before multiplying.

Divide by the common factors 6, x and y.

$\frac{\cancel{6}{x}^2{y}^4}{\cancel{12}}\cdot \frac{3x^3{y}^2}{\cancel{x}\cancel{y}}$

Step 3. Simplify the expression.

Further simplify the expression.

$\begin{array}{c}\frac{6x^2{y}^4}{12}\cdot \frac{3x^3{y}^2}{xy}=\frac{x{y}^3}{2}\cdot 3x^3{y}^2\\ =\frac{3x^4{y}^5}{2}\end{array}$

Therefore, the final product of the expression is $\frac{3x^4{y}^5}{2}$.