Question

Simplify${(-2r^{2}s)}^3\left(3r{s}^2\right)$ assuming that no variable equal to 0 .

Short answer

The simplified value of expression is$-24r^7{s}^5$ .

Step-by-step solution

Step 1. Write down the given expression.

The given expressiomn to simplify is ${(-2r^{2}s)}^3\left(3r{s}^2\right)$.

Step 2. Simplify the given expression.

Simplifying ${(-2r^{2}s)}^3\left(3r{s}^2\right)$gives,

$\begin{array}{c}{(-2r^{2}s)}^3\left(3r{s}^2\right)={(-2)}^3{\left(r^{2}s\right)}^3\left(3r{s}^2\right)\\ =-8{\left(r\right)}^6{\left(s\right)}^3\left(3\right)\left(r\right){\left(s\right)}^2\\ =(-8\times 3){\left(r\right)}^{6+1}{\left(s\right)}^{3+2}\mathrm{....}(\text{Using}{x}^a\times x^b=x^{a+b})\\ =-24r^7{s}^5\end{array}$

Step 3. Conclusion.

The simplified value of expression is $-24r^7{s}^5$.