Q. 153 - Intermediate Algebra

Question

Simplify ${\left(3m^{2}n\right)}^2{\left(2m{n}^5\right)}^4$

Step-by-Step Solution

Answer

Simplified expression is $144m^8{n}^{22}$

Step 1. Given information

${\left(3m^{2}n\right)}^2{\left(2m{n}^5\right)}^4$

Step 2

Here

$$\begin{gathered} {\left(3m^{2}n\right)}^2{\left(2m{n}^5\right)}^4={\left(3\right)}^2{\left(m^2\right)}^2{\left(n\right)}^2{\left(2\right)}^4{\left(m\right)}^4{\left(n^5\right)}^4 \\ =9\times m^{2\times 2}\times n^2\times 16\times m^4\times n^{5\times 4} \\ =144\times m^4\times n^2\times m^4\times n^{20} \\ =144\times m^{4+4}\times n^{2+20} \\ =144m^8{n}^{22} \end{gathered}$$