Express the prime factorization of 54 as a product of prime numbers with exponents.(1 point)

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1 answer

To find the prime factorization of 54, we can break it down step by step:

  1. 54 is an even number, so we can start by dividing it by 2: \[ 54 \div 2 = 27 \]

  2. Next, we factor 27. Since 27 is not even, we try the next smallest prime number, which is 3: \[ 27 \div 3 = 9 \]

  3. We continue factoring 9, which is also divisible by 3: \[ 9 \div 3 = 3 \]

  4. Finally, we factor 3, which is already a prime number: \[ 3 \div 3 = 1 \]

Now we can compile these factors together:

  • We have used the prime factor 2 once.
  • We have used the prime factor 3 three times.

Thus, the prime factorization of 54 is: \[ 54 = 2^1 \times 3^3 \]

So, the answer is: \[ \boxed{2^1 \times 3^3} \]