Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (4 + 2) ÷ 5 x 2 - 4²
P: 3 + (6) ÷ 5 x 2 - 4²
E: 3 + 6 ÷ 5 x 2 - 16
MD: 3 + \( \frac{6}{5} \) x 2 - 16
MD: 3 + \( \frac{12}{5} \) - 16
AS: \( \frac{15}{5} \) + \( \frac{12}{5} \) - 16
AS: \( \frac{27}{5} \) - 16
AS: \( \frac{27 - 80}{5} \)
\( \frac{-53}{5} \)
-10\(\frac{3}{5}\)

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{10} \) = 3\(\frac{3}{10}\) 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 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 430 small cakes are needed for the party so \( \frac{430}{28} \) = 15\(\frac{5}{14}\) 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 + 16 = 20 cooks.

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).

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:

-5z⁶ x 9z⁶
(-5 x 9)z^{(6 + 6)}
-45z¹²

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.