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).

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

\( \frac{35\sqrt{15}}{5\sqrt{3}} \)
\( \frac{35}{5} \) \( \sqrt{\frac{15}{3}} \)
7 \( \sqrt{5} \)

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 9 people needing transportation leaving 9 - 6 = 3 who will have to find other transportation.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 7}{5 x 7} \) - \( \frac{4 x 5}{7 x 5} \)

\( \frac{49}{35} \) - \( \frac{20}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{49 - 20}{35} \) = \( \frac{29}{35} \) = \(\frac{29}{35}\)

To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{3 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 2