What is the prime factorization of 90 using exponents?

The prime factorization of 90 can be found by dividing the number by prime numbers until we reach 1. Let’s break it down step-by-step.

First, we start by dividing 90 by the smallest prime number, which is 2:

• 90 ÷ 2 = 45

Next, we continue with 45. The smallest prime number we can use here is 3:

• 45 ÷ 3 = 15

Now, we take 15 and divide again by 3:

• 15 ÷ 3 = 5

Finally, we reach 5, which is itself a prime number:

• 5 ÷ 5 = 1

Putting it all together, we can express 90 as a product of its prime factors:

90 = 2 × 3 × 3 × 5

Using exponents, we can write this as:

90 = 2¹ × 3² × 5¹

So, the prime factorization of 90 using exponents is 2¹ × 3² × 5¹.