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

\( \frac{3}{6} \) x \( \frac{2}{5} \) = \( \frac{3 x 2}{6 x 5} \) = \( \frac{6}{30} \) = \(\frac{1}{5}\)

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:

-9b⁴ x 4b⁶
(-9 x 4)b^{(4 + 6)}
-36b¹⁰

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 fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{5 \text{ gallons}}{1 \text{ gallons}} \) = 5

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