Question

Find the product: $\left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)$

Answer 1

Simplify using the rules of exponents:

The given expression is $\left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)$.

It can be simplified as follows,

$\left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-\frac{10}{3}\times p\times q^3\times \frac{6}{5}\times p^3\times q$

$\Rightarrow \left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-\frac{10}{3}\times \frac{6}{5}\times p\times p^3\times q^3\times q$

$\Rightarrow \left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-\frac{10}{3}\times \frac{6}{5}\times p^{1+3}\times q^{3+1}$ $\left[\because a^m\times a^n=a^{m+n}\right]$

$$\begin{gathered} \Rightarrow \left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-\frac{2}{1}\times \frac{2}{1}\times p^4\times q^4 \\ \Rightarrow \left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-2\times 2\times p^4\times q^4 \\ \Rightarrow \left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)=-4p^4{q}^4 \end{gathered}$$

Hence, the value of the product $\left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)$ is $-4p^4{q}^4$.