Simplify each expression using the laws of exponents to see if they are equal to the given number.
Remember the following:
[tex]\begin{gathered} a^n\times a^m=a^{n+m} \\ \frac{a^n}{a^m}=a^{n-m} \end{gathered}[/tex]
First expression:
[tex]\begin{gathered} (2\times10^8)(2\times10^{-2})=2\times2\times10^8\times10^{-2} \\ =4\times10^{8-2} \\ =4\times10^6 \end{gathered}[/tex]
Second expression:
[tex]\begin{gathered} 40\times10^5=4\times10\times10^5 \\ =4\times10^{5+1} \\ =4\times10^6 \end{gathered}[/tex]
Third expresion:
[tex]\begin{gathered} 40^6=(4\times10)^6 \\ =4^6\times10^6 \\ =4096\times10^6 \end{gathered}[/tex]
Fourth expression:
[tex]\begin{gathered} 400,000=4\times100,000 \\ =4\times10^5 \end{gathered}[/tex]
Fifth expression:
[tex]\begin{gathered} \frac{1.2\times10^9}{3\times10^2}=\frac{1.2\times10\times10^8}{3\times10^2} \\ =\frac{12\times10^8}{3\times10^2} \\ =\frac{12}{3}\times\frac{10^8}{10^2} \\ =4\times10^{8-2} \\ =4\times10^6 \end{gathered}[/tex]
