Given:
The given number is 200.
To find:
The product of prime factors in the index form for the given number.
Solution:
Prime factorization of 200 is
[tex]2 | 200\\\overline{2}|\overline{100}\\\overline{2}|\overline{50}\\\overline{5}|\overline{25}\\\overline{5}|\overline{5}\\\ \text{}\ \ |\overline{1}[/tex]
So, 200 can be written as the product of this prime factors.
[tex]200=2\times 2\times 2\times 5\times 5[/tex]
[tex]200=2^3\times 5^2[/tex]
Therefore, the number 200 can be written as [tex]2^3\times 5^2[/tex].
