Factoring Monomials

We know that the Fundamental Theorem of Arithmetic states that any whole number can be written uniquely as a product of prime factors. What about factoring monomials?

The "prime factorization" of a monomial is its expression as a product of prime numbers, single variables, and (possibly) a –1.

Example:

Find the prime factorization of –27p2qr5.

27 can be written as 3 · 3 · 3. Then just write the powers out the long way, and multiply by –1.

–27p2qr5 = –1 · 3 · 3 · 3 · p · p · q · r · r · r · r · r