The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

-7b⁴ + 1b⁴
(-7 + 1)b⁴
-6b⁴

The greatest common factor (GCF) is the greatest factor that divides two integers.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{4 x 5}{8 x 5} \) + \( \frac{9 x 4}{10 x 4} \)

\( \frac{20}{40} \) + \( \frac{36}{40} \)

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

\( \frac{20 + 36}{40} \) = \( \frac{56}{40} \) = 1\(\frac{2}{5}\)

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

\( \frac{2}{7} \) ÷ \( \frac{1}{8} \) = \( \frac{2}{7} \) x \( \frac{8}{1} \)

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

\( \frac{2}{7} \) x \( \frac{8}{1} \) = \( \frac{2 x 8}{7 x 1} \) = \( \frac{16}{7} \) = 2\(\frac{2}{7}\)