Final answer:
The prime factorization of 81 is found by repeatedly dividing by the prime number 3 until we reach 1, which results in the factors 3, 3, 3, and 3. Using exponents, this is expressed as 3 to the power of 4, or 3´.
Step-by-step explanation:
Prime Factorization of 81
To find the prime factorization of 81 using exponents, we start by dividing 81 by the smallest prime number that can evenly divide it. Since 81 is a multiple of 3, we start with 3 and continue dividing:
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Once we reach 1, we have found all the prime factors. Each division by 3 shows that 3 is a prime factor of 81, and since we divided by 3 a total of four times, we can express this using exponents as 3⁴.
Therefore, the prime factorization of 81 is 3⁴, which means 3 raised to the power of 4, or 3 × 3 × 3 × 3, which equals 81.