Question 1Step 1: Problem
[tex]\text{Factor 8mn}^2\text{ + 12mn}[/tex]Step 2: Concept
Factor the highest common factor out.
Step 3: Method
[tex]8mn^2\text{ + 12mn = 4mn( 2n + 3)}[/tex]Step 4: Final answer
4mn(2n + 3)
Question 2
Step 1: Question
[tex]\text{Simplify }\frac{(1.24\text{ }\times10^2\text{ ) (3.6 }\times10^{-3})}{1.8\text{ }\times\text{ 10}}[/tex]Step 2: Concept
Apply laws of exponent
[tex]\begin{gathered} \text{Division law } \\ \frac{m^x}{m^y}=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }\times m^y=m^{x\text{ + y}} \end{gathered}[/tex]Step 3: Method
[tex]\begin{gathered} =\text{ }\frac{(1.24\text{ }\times10^2\text{ )(3.6 }\times10^{-3})}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }\times\text{ 3.6 }\times10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{-1}}{18} \\ =\text{ }\frac{4.464}{18}\text{ }\times10^{-1} \\ =\text{ 0.248 }\times10^{-1} \\ =\text{ 2.48 }\times10^{-2} \end{gathered}[/tex]Step 4: Final answer
Option D is the correct answer
[tex]2.48\text{ }\times10^{-2}[/tex]
