Here are examples for the two different types of problems in this topic.

Example 1: Prime factoring with exponents

Convert the fraction so that both the numerator and denominator are expressed in terms of their prime factors. Do not simplify
Example: 12/25 = (2^2 * 3)/(5^2)

8 18

=

2 * 2 * 2 2 * 2 * 3 * 3

=

2^3 2^2 * 3^2

The answer is

8 18

=

Example 2: Fraction simplification with prime factoring

In the first set of fraction answer boxes, put in the numerator and denominator expressed in terms of their prime factors. In the second set of fraction answer boxes, take out common factors and put the remaining factors. For the last set of answer boxes, multiply back out the factors to end up with the final reduced fraction.
i.e. 25/70 = (5^2)/(2 * 5 * 7) = 5/(2 * 7) = 5/14

27 45

= = =

Find the prime factorization for the numerator and the denominator using exponetns.

27 45

=

3 * 3 * 3 3 * 3 * 5

=

3^3 3^2 * 5

Simplify the fraction.

27 45

=

3^3 3^2 * 5

=

3 3^3 3^2 * 5

=

3 5

The answer is

27 45

= = =