Question

which of the following shkws the prime factorization of using 200 using exponential notation?2^3 × 5^2 2×10^2 8× 252^2 *5^2

Answer 1

Notice the following:

`\begin{gathered} 200=2*100 \\ =2*10^2 \end{gathered}`

On the other hand, we know that 10=2*5. Then:

`\begin{gathered} 2*10^2=2*(2\cdot5)^2 \\ =2*2^2\cdot5^2 \\ =2^3\cdot5^2 \end{gathered}`

Therefore, the prime factorization of 200 using exponential notation, is:

`2^3\cdot5^2`