Question
what numbers i can use to make in exponents a prime factorization of 1000
Answers
GPT-4o mini
To express \(1000\) in terms of its prime factorization using exponents, we first need to break it down into its prime factors.
1. We can start by dividing \(1000\) by \(10\):
\[
1000 = 10 \times 100
\]
\[
100 = 10 \times 10
\]
Thus,
\[
1000 = 10 \times 10 \times 10 = 10^3
\]
2. Next, we factor \(10\) into its prime factors:
\[
10 = 2 \times 5
\]
So we have:
\[
1000 = (2 \times 5)^3
\]
3. Applying the exponent to both prime factors:
\[
1000 = 2^3 \times 5^3
\]
Thus, the prime factorization of \(1000\) using exponents is:
\[
1000 = 2^3 \times 5^3
\]
1. We can start by dividing \(1000\) by \(10\):
\[
1000 = 10 \times 100
\]
\[
100 = 10 \times 10
\]
Thus,
\[
1000 = 10 \times 10 \times 10 = 10^3
\]
2. Next, we factor \(10\) into its prime factors:
\[
10 = 2 \times 5
\]
So we have:
\[
1000 = (2 \times 5)^3
\]
3. Applying the exponent to both prime factors:
\[
1000 = 2^3 \times 5^3
\]
Thus, the prime factorization of \(1000\) using exponents is:
\[
1000 = 2^3 \times 5^3
\]