veronicaibloom veronicaibloom
  • 24-01-2019
  • Mathematics
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how do you write the prime factorization in exponent form for example 27

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remotecontrolbrain
remotecontrolbrain remotecontrolbrain
  • 24-01-2019

Answer:

[tex]27 = 3 \cdot 9 = 3 \cdot 3 \cdot 3 = 3^3[/tex]

Step-by-step explanation:

In general, let n be a natural number, and [tex]p_1, p_2, ..., p_k[/tex] be a set of its prime factors, each with a multiplicity [tex]k_1, k_2, ..., k_k[/tex] (multiplicity being the "number of times a given prime shows up as a factor"). Then every number can be written as a product in an exponential form:

[tex]n = p_1^{k_1}\cdot p_2^{k_2}\cdot\cdot\cdot p_k^{k_k}[/tex]

In the example of 27, the p_1=3 and k_1 = 3.

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