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`

Step-by-step explanation

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

Step 1

remember:

`\begin{gathered} (a^m)/(a^n)=a^(m-n) \\ \\ (a^mb^x)/(a^nb^y)=a^(m-n)b^(x-y) \end{gathered}`

the division is

`\begin{gathered} (9\cdot10^4)/(3\cdot10^2) \\ \text{Also} \\ 9=3^2 \\ so, \\ (9\cdot10^4)/(3\cdot10^2)=(3^2\cdot10^4)/(3\cdot10^2) \end{gathered}`

Step 2

`\begin{gathered} (3^2\cdot10^4)/(3\cdot10^2) \\ \\ (3^2\cdot10^4)/(3\cdot10^2)=3^(2-1)\cdot10^(4-2) \\ (3^2\cdot10^4)/(3\cdot10^2)=3\cdot10^2 \\ (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