If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 36 large cakes are needed for the party so \( \frac{36}{4} \) = 9 cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 18 x 2 = 36 small cakes during that time. 340 small cakes are needed for the party so \( \frac{340}{36} \) = 9\(\frac{4}{9}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 9 + 10 = 19 cooks.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{3 x 5}{8 x 5} \) + \( \frac{5 x 4}{10 x 4} \)

\( \frac{15}{40} \) + \( \frac{20}{40} \)

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

\( \frac{15 + 20}{40} \) = \( \frac{35}{40} \) = \(\frac{7}{8}\)

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

5a² x 4a⁷
(5 x 4)a^{(2 + 7)}
20a⁹

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.