A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{12} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 330 small cakes are needed for the party so \( \frac{330}{56} \) = 5\(\frac{25}{28}\) 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 4 + 6 = 10 cooks.

To add these radicals together their radicands must be the same:

7\( \sqrt{175} \) + 5\( \sqrt{7} \)
7\( \sqrt{25 \times 7} \) + 5\( \sqrt{7} \)
7\( \sqrt{5^2 \times 7} \) + 5\( \sqrt{7} \)
(7)(5)\( \sqrt{7} \) + 5\( \sqrt{7} \)
35\( \sqrt{7} \) + 5\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{98}{8} \) = 12\(\frac{1}{4}\)

So, it will take 12 full vans and one partially full van to transport the entire team making a total of 13 vans.

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{64} \) = \( \frac{\frac{16}{16}}{\frac{64}{16}} \) = \( \frac{1}{4} \)