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Express the prime factorization of 54 as a product of prime numbers with exponents
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put that into one number with exponents
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express prime factorization of 144 as a product of prime factors by filling in the missing exponents after the caret
2^_ * 3^_ = 144
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what times three = 72
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express 48 as a product of prime numbers using exponents
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the number 100 expressed as its prime numbers is
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The prime factorization of 54 is 2^1 * 3^3.
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The prime factorization of 54 can be expressed as 2^1 * 3^3, which can be written as 2 * 3^3.
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To express the prime factorization of 144, we need to determine the exponents for each prime factor.

Starting with 2, we can divide 144 by 2 repeatedly until we reach a quotient that is not divisible by 2.
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 2 = 4.5

Since 4.5 is not a whole number, we know that 2 is no longer a factor of 144.

Moving to 3, we follow a similar process:
144 ÷ 3 = 48
48 ÷ 3 = 16
16 ÷ 3 = 5.333

Again, 5.333 is not a whole number, so 3 is no longer a factor of 144.

Therefore, the prime factorization of 144 is 2^4 * 3^2.
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The number that, when multiplied by 3, equals 72 is 24.

3 * 24 = 72
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The prime factorization of 48 is 2^4 * 3^1.
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The prime factorization of 100 is 2^2 * 5^2.