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:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)

To fill a 16 gallon tank exactly halfway you'll need 8 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{8 \text{ gallons}}{2 \text{ gallons}} \) = 4

The amount of flour you need is (2\(\frac{5}{8}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{21}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{19}{8} \) cups
2\(\frac{3}{8}\) cups

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

3 + (4 + 4) ÷ 2 x 2 - 3²
P: 3 + (8) ÷ 2 x 2 - 3²
E: 3 + 8 ÷ 2 x 2 - 9
MD: 3 + \( \frac{8}{2} \) x 2 - 9
MD: 3 + \( \frac{16}{2} \) - 9
AS: \( \frac{6}{2} \) + \( \frac{16}{2} \) - 9
AS: \( \frac{22}{2} \) - 9
AS: \( \frac{22 - 18}{2} \)
\( \frac{4}{2} \)
2

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).