Question
Represent number 200 in the form 2n
.5m
.5m
Answers
GPT-4o mini
To represent the number 200 in the form \( 2^n \cdot 5^m \), we can start by factoring 200 into its prime factors.
1. First, let's find the prime factorization of 200:
\[
200 = 2 \times 100
\]
\[
100 = 2 \times 50
\]
\[
50 = 2 \times 25
\]
\[
25 = 5 \times 5
\]
So, combining these results:
\[
200 = 2^3 \times 5^2
\]
2. In this case, we have:
- \( n = 3 \) (the power of 2),
- \( m = 2 \) (the power of 5).
Thus, we can express 200 in the form \( 2^n \cdot 5^m \) as:
\[
200 = 2^3 \cdot 5^2
\]
1. First, let's find the prime factorization of 200:
\[
200 = 2 \times 100
\]
\[
100 = 2 \times 50
\]
\[
50 = 2 \times 25
\]
\[
25 = 5 \times 5
\]
So, combining these results:
\[
200 = 2^3 \times 5^2
\]
2. In this case, we have:
- \( n = 3 \) (the power of 2),
- \( m = 2 \) (the power of 5).
Thus, we can express 200 in the form \( 2^n \cdot 5^m \) as:
\[
200 = 2^3 \cdot 5^2
\]