Question

i) write the prime factorization of 7. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Identify if 7 is prime

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. 7 is greater than 1, and its only divisors are 1 and 7. So 7 is a prime number.

Step2: Prime factorization of a prime number

The prime factorization of a prime number \( p \) is just \( p \) itself (since it can't be factored into smaller prime factors). So for 7, the prime factorization is \( 7 \) (with an exponent of 1, which we usually don't write explicitly when the exponent is 1, but since the example had exponents when appropriate, and here the exponent is 1, we can write it as \( 7^1 \) or just \( 7 \); following the example's style, we can write it as \( 7 \)).

Answer:

\( 7 \)