Evaluate;
[tex]\frac{7.5\times10^{12}}{2.0\times10^5}[/tex]Solution:
Re-express the expression as;
[tex]\begin{gathered} \frac{7.5\times10^{12}}{2.0\times10^5}=\frac{75\times10^{-1}\times10^{12}}{2.0\times10^5} \\ \frac{7.5\times10^{12}}{2.0\times10^5}=\frac{75}{2}\times\frac{10^{11}}{10^5} \\ \end{gathered}[/tex]Apply division law of indices;
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex][tex]\begin{gathered} \frac{7.5\times10^{12}}{2.0\times10^5}=37.5\times10^{11-5} \\ \frac{7.5\times10^{12}}{2.0\times10^5}=3.75\times10^1\times10^6 \end{gathered}[/tex]
Apply the multiplication law of indices;
[tex]a^b\times a^c=a^{b+c}[/tex][tex]\begin{gathered} \frac{7.5\times10^{12}}{2.0\times10^5}=3.75\times10^{1+6} \\ \frac{7.5\times10^{12}}{2.0\times10^5}=3.75\times10^7 \\ \end{gathered}[/tex]ANSWER:
[tex]3.75\times10^7[/tex]