Question

How do you write the prime factorization in exponent form for example 27

Answer 1

`27 = 3 \cdot 9 = 3 \cdot 3 \cdot 3 = 3^3`

Explanation:

In general, let n be a natural number, and
`p_1, p_2, ..., p_k` be a set of its prime factors, each with a multiplicity
`k_1, k_2, ..., k_k` (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:

`n = p_1^(k_1)\cdot p_2^(k_2)\cdot\cdot\cdot p_k^(k_k)`

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