Section 1: Prime Factorization

Every natural number can be written as a product of prime numbers. For example,

50 = 2\cdot 5\cdot 5

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When the product is written with exponents instead of writing out repeated multiplication, we say we have factored the original number into "prime powers."

Directions:

Factor each of the numerator and denominator into a product of prime powers. Then use the product and quotient rules for exponential expressions to reduce the fraction. Keep everything expressed as a product of prime powers or a ratio of those products.