To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 9 factors [1, 2, 3, 4, 6, 9, 12, 18, 36] making 36 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{72} \) = \( \frac{\frac{36}{36}}{\frac{72}{36}} \) = \( \frac{1}{2} \)

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 24 - 12 = 12 new staff for the busy season.

The greatest common factor (GCF) is the greatest factor that divides two integers.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 7}{5 x 7} \) - \( \frac{2 x 5}{7 x 5} \)

\( \frac{28}{35} \) - \( \frac{10}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{28 - 10}{35} \) = \( \frac{18}{35} \) = \(\frac{18}{35}\)