Question

Find the product: $\left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)$

Answer 1

Simplify using the rules of exponents:

The given expression is $\left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)$.

It can be simplified as follows,

$\left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-\frac{2}{3}\times x\times y\times \frac{9}{10}\times x^2\times y^2$

$\Rightarrow \left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-\frac{2}{3}\times \frac{9}{10}\times x\times x^2\times y\times y^2$

$\Rightarrow \left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-\frac{2}{3}\times \frac{9}{10}\times x^{1+2}\times y^{1+2}$ $\left[\because a^m\times a^n=a^{m+n}\right]$

$$\begin{gathered} \Rightarrow \left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-\frac{1}{1}\times \frac{3}{5}\times x^3\times y^3 \\ \Rightarrow \left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-1\times \frac{3}{5}\times x^3\times y^3 \\ \Rightarrow \left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)=-\frac{3}{5}{x}^3{y}^3 \end{gathered}$$

Hence, the value of the product of $\left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)$ is $-\frac{3}{5}{x}^3{y}^3$.