Question

1. communicate mathematical ideas camille simplified an expression as shown. discuss why this method is justified. $\frac{6cdot10^{5}}{3cdot10^{2}}=\frac{6}{3}cdot\frac{10^{5}}{10^{2}} = 2cdot10^{3}=2000$

Explanation:

Step1: Use fraction - division property

$\frac{6\cdot10^{5}}{3\cdot10^{2}}=\frac{6}{3}\cdot\frac{10^{5}}{10^{2}}$ is justified by the property $\frac{a\cdot c}{b\cdot d}=\frac{a}{b}\cdot\frac{c}{d}$ where $a = 6$, $b = 3$, $c=10^{5}$, and $d = 10^{2}$.

Step2: Simplify non - exponential part

$\frac{6}{3}=2$ since $6\div3 = 2$.

Step3: Use exponent rule

$\frac{10^{5}}{10^{2}}=10^{5 - 2}=10^{3}$ by the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$ where $a = 10$, $m = 5$, and $n = 2$.

Step4: Calculate final result

$2\cdot10^{3}=2\times1000 = 2000$

Answer:

The method is justified by the fraction - division property, non - exponential simplification, and the exponent rule for division. The result of $\frac{6\cdot10^{5}}{3\cdot10^{2}}$ is 2000.