To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{5 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 2

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 divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{16\sqrt{27}}{8\sqrt{9}} \)
\( \frac{16}{8} \) \( \sqrt{\frac{27}{9}} \)
2 \( \sqrt{3} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{4} \) x 6\( \sqrt{8} \)
(9 x 6)\( \sqrt{4 \times 8} \)
54\( \sqrt{32} \)

Now we need to simplify the radical:

54\( \sqrt{32} \)
54\( \sqrt{2 \times 16} \)
54\( \sqrt{2 \times 4^2} \)
(54)(4)\( \sqrt{2} \)
216\( \sqrt{2} \)