To determine the exponent of the prime factor 3 in the prime factorization of 54, we first need to factor 54 into its prime components.
Starting with 54:
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We can divide 54 by 2 (the smallest prime number): \[ 54 \div 2 = 27 \] So, 54 can be expressed as \( 54 = 2 \times 27 \).
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Next, we factor 27: \[ 27 \div 3 = 9 \quad \text{(because 27 is divisible by 3)} \] \[ 27 = 3 \times 9 \]
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Now we factor 9: \[ 9 \div 3 = 3 \] \[ 9 = 3 \times 3 \]
Putting it all together, we have: \[ 54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3 \]
From the factorization, we see that the prime factor 3 appears 3 times. Thus, the exponent of the prime factor 3 in the prime factorization of 54 is:
\[ \boxed{3} \]
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