To add or subtract terms with exponents, both the base and the exponent must be the same. If the base and the exponent are the same, add or subtract the coefficients and retain the base and exponent. For example, 3x² + 2x² = 5x² and 3x² - 2x² = x² but x² + x⁴ and x⁴ - x² cannot be combined.

The average (or mean) of a group of terms is the sum of the terms divided by the number of terms. Average = \({a_1 + a_2 + ... + a_n \over n}\)

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To multiply terms with the same base, multiply the coefficients and add the exponents. To divide terms with the same base, divide the coefficients and subtract the exponents. For example, 3x² x 2x² = 6x⁴ and \({8x^5 \over 4x^2} \) = 2x^(5-2) = 2x³.

A rate is a ratio that compares two related quantities. Common rates are speed = \({distance \over time}\), flow = \({amount \over time}\), and defect = \({errors \over units}\).