The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 25 large cakes are needed for the party so \( \frac{25}{15} \) = 1\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 310 small cakes are needed for the party so \( \frac{310}{30} \) = 10\(\frac{1}{3}\) 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 + 11 = 13 cooks.

To multiply terms with radicals, multiply the coefficients and radicands separately:

6\( \sqrt{4} \) x 6\( \sqrt{9} \)
(6 x 6)\( \sqrt{4 \times 9} \)
36\( \sqrt{36} \)

Now we need to simplify the radical:

36\( \sqrt{36} \)
36\( \sqrt{6^2} \)
(36)(6)
216

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{25\sqrt{12}}{5\sqrt{6}} \)
\( \frac{25}{5} \) \( \sqrt{\frac{12}{6}} \)
5 \( \sqrt{2} \)