Notice the following:
[tex]\begin{gathered} 200=2\times100 \\ =2\times10^2 \end{gathered}[/tex]
On the other hand, we know that 10=2*5. Then:
[tex]\begin{gathered} 2\times10^2=2\times(2\cdot5)^2 \\ =2\times2^2\cdot5^2 \\ =2^3\cdot5^2 \end{gathered}[/tex]
Therefore, the prime factorization of 200 using exponential notation, is:
[tex]2^3\cdot5^2[/tex]
