Personally, I would recommend reading this as a fraction, and splitting up mantissa from the power of 10. (Mantissa refers to the number 1.23 in [tex]1.23\times10^n[/tex].)
[tex]\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = \dfrac{3.6 \times 10^{-5}}{9 \times 10^{-7}} = \dfrac{3.6}9 \times \dfrac{10^{-5}}{10^{-7}}[/tex]
Now just reduce each fraction:
[tex]\dfrac{3.6}9 = \dfrac{36}{90} = \dfrac25 = 0.4[/tex]
[tex]\dfrac{10^{-5}}{10^{-7}} = 10^{-5-(-7)} = 10^{-5+7} = 10^2[/tex]
So
[tex]\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = 0.4 \times 10^2 = \boxed{4 \times 10^1}[/tex]
since [tex]0.4\times10^2 = 0.4 \times 100 = 40 = 4 \times 10[/tex].
