what numbers i can use to make in exponents a prime factorization of 1000

Answer 1

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: \[ 1000 = 2^3 \times 5^3 \]