A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

1x⁶ - 8x⁶
(1 - 8)x⁶
-7x⁶

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. 22 large cakes are needed for the party so \( \frac{22}{4} \) = 5\(\frac{1}{2}\) 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 2 hours, a single cook can bake 17 x 2 = 34 small cakes during that time. 420 small cakes are needed for the party so \( \frac{420}{34} \) = 12\(\frac{6}{17}\) 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 6 + 13 = 19 cooks.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{7} \) ÷ \( \frac{4}{5} \) = \( \frac{1}{7} \) x \( \frac{5}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{7} \) x \( \frac{5}{4} \) = \( \frac{1 x 5}{7 x 4} \) = \( \frac{5}{28} \) = \(\frac{5}{28}\)