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

\( \frac{4}{6} \) ÷ \( \frac{3}{5} \) = \( \frac{4}{6} \) x \( \frac{5}{3} \)

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

\( \frac{4}{6} \) x \( \frac{5}{3} \) = \( \frac{4 x 5}{6 x 3} \) = \( \frac{20}{18} \) = 1\(\frac{1}{9}\)

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 6 + 10 + 6}{4} \) = \( \frac{32}{4} \) = 8

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:

4z⁷ + 8z⁷
(4 + 8)z⁷
12z⁷

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.