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

(\( \frac{18}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{9}{8} \) cups
1\(\frac{1}{8}\) cups

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 2}{2 x 2} \) + \( \frac{3 x 1}{4 x 1} \)

\( \frac{8}{4} \) + \( \frac{3}{4} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{8 + 3}{4} \) = \( \frac{11}{4} \) = 2\(\frac{3}{4}\)

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:

-6b⁴ x 9b⁵
(-6 x 9)b^{(4 + 5)}
-54b⁹

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.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.