Q26. - Algebra 2

Question

Simplify the expression $\frac{2x^{3}y}{z^5}÷{\left(\frac{4xy}{z^3}\right)}^2$.

Step-by-Step Solution

Answer

The simplified value of expression is$\frac{xz}{8y}$.

Step 1. Write down the given expression.

The given expression is $\frac{2x^{3}y}{z^5}÷{\left(\frac{4xy}{z^3}\right)}^2$.

Step 2. Simplify the expression.

The given expression $\frac{2x^{3}y}{z^5}÷{\left(\frac{4xy}{z^3}\right)}^2$ is simplified as:

$\begin{array}{l}\frac{2x^{3}y}{z^5}÷{\left(\frac{4xy}{z^3}\right)}^2=\frac{2x^{3}y}{z^5}\times {\left(\frac{z^3}{4xy}\right)}^2\\ =\frac{2x^{3}y}{z^5}\times \frac{z^6}{16x^2{y}^2}\\ =\frac{2}{16}\times \frac{x^{3}y{z}^6}{x^2{y}^2{z}^5}\\ =\frac{xz}{8y}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{xz}{8y}$.