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 subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{4 x 3}{3 x 3} \) - \( \frac{6 x 1}{9 x 1} \)

\( \frac{12}{9} \) - \( \frac{6}{9} \)

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

\( \frac{12 - 6}{9} \) = \( \frac{6}{9} \) = \(\frac{2}{3}\)

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:

-9z⁶ x z⁴
(-9 x 1)z^{(6 + 4)}
-9z¹⁰

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

4 + (3 + 4) ÷ 4 x 2 - 3²
P: 4 + (7) ÷ 4 x 2 - 3²
E: 4 + 7 ÷ 4 x 2 - 9
MD: 4 + \( \frac{7}{4} \) x 2 - 9
MD: 4 + \( \frac{14}{4} \) - 9
AS: \( \frac{16}{4} \) + \( \frac{14}{4} \) - 9
AS: \( \frac{30}{4} \) - 9
AS: \( \frac{30 - 36}{4} \)
\( \frac{-6}{4} \)
-1\(\frac{1}{2}\)

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:

-1c⁷ - 2c⁷
(-1 - 2)c⁷
-3c⁷