Question

compare 9 X 10 to the 4th power with 3 * 10 to the second power

Answer 1

$9\cdot10^4\text{ is 300 times 3}\cdot10^2$

Explanation

$\begin{gathered} 9\cdot10^4 \\ 3\cdot10^2 \end{gathered}$

Step 1

remember:

$\begin{gathered} \frac{a^m}{a^n}=a^{m-n} \\ \\ \frac{a^mb^x}{a^nb^y}=a^{m-n}b^{x-y} \end{gathered}$

the division is

$\begin{gathered} \frac{9\cdot10^4}{3\cdot10^2} \\ \text{Also} \\ 9=3^2 \\ so, \\ \frac{9\cdot10^4}{3\cdot10^2}=\frac{3^2\cdot10^4}{3\cdot10^2} \end{gathered}$

Step 2

$\begin{gathered} \frac{3^2\cdot10^4}{3\cdot10^2} \\ \\ \frac{3^2\cdot10^4}{3\cdot10^2}=3^{2-1}\cdot10^{4-2} \\ \frac{3^2\cdot10^4}{3\cdot10^2}=3\cdot10^2 \\ \frac{3^2\cdot10^4}{3\cdot10^2}=300 \end{gathered}$

it means

$9\cdot10^4\text{ is 300 times 3}\cdot10^2$

I hope this helps you