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

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
4

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 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{7 x 9}{5 x 9} \) - \( \frac{5 x 5}{9 x 5} \)

\( \frac{63}{45} \) - \( \frac{25}{45} \)

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

\( \frac{63 - 25}{45} \) = \( \frac{38}{45} \) = \(\frac{38}{45}\)

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{16} \) = 1\(\frac{13}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 210 small cakes are needed for the party so \( \frac{210}{68} \) = 3\(\frac{3}{34}\) 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 2 + 4 = 6 cooks.

The amount of flour you need is (2\(\frac{1}{2}\) - \(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{20}{8} \) - \( \frac{5}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups