To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-6b^5}{b^2} \)
\( \frac{-6}{1} \) b^{(5 - 2)}
-6b³

First, solve for \( \left|b + 1\right| \):

\( \left|b + 1\right| \) - 6 = 8
\( \left|b + 1\right| \) = 8 + 6
\( \left|b + 1\right| \) = 14

The value inside the absolute value brackets can be either positive or negative so (b + 1) must equal + 14 or -14 for \( \left|b + 1\right| \) to equal 14:

So, b = -15 or b = 13.

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

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

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

\( \frac{2}{8} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{8 x 1} \) = \( \frac{14}{8} \) = 1\(\frac{3}{4}\)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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).