What is the prime factorization of 18 using exponents?

The prime factorization of 18 is expressed as 2¹ × 3².

To arrive at this, we first need to identify the prime factors of 18. We start dividing 18 by the smallest prime number, which is 2:

• 18 ÷ 2 = 9

Now, we have 2 as one of our prime factors with an exponent of 1 since we divided by it once. Next, we factor the result, 9:

• 9 is not divisible by 2, so we try the next prime number, which is 3:
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Here, we find that 9 can be expressed as 3 × 3, which means 3 is a prime factor that is repeated twice. Thus, we can write 9 as 3².

Combining these factors gives us the complete prime factorization of 18 as 2¹ × 3².