Q. 152 - Intermediate Algebra

Question

Simplify ${\left(\frac{1}{3}{m}^3{n}^2\right)}^4{\left(9m^8{n}^3\right)}^2$

Step-by-Step Solution

Answer

Simplified expression is $m^{28}{n}^{14}$

Step 1. Given information

${\left(\frac{1}{3}{m}^3{n}^2\right)}^4{\left(9m^8{n}^3\right)}^2$

Step 2

$$\begin{gathered} {\left(\frac{1}{3}{m}^3{n}^2\right)}^4{\left(9m^8{n}^3\right)}^2={\left(\frac{1}{3}\right)}^4{\left(m^3\right)}^4{\left(n^2\right)}^4{\left(9\right)}^2{\left(m^8\right)}^2{\left(n^3\right)}^2 \\ =\frac{1}{3^4}\times m^{3\times 4}\times n^{2\times 4}\times 9^2\times m^{8\times 2}\times n^{3\times 2} \\ =\frac{1}{81}\times m^{12}\times n^8\times 81\times m^{16}\times n^6 \\ =m^{28}{n}^{14} \end{gathered}$$