To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{2b^8}{9b^3} \)
\( \frac{2}{9} \) b^{(8 - 3)}
\(\frac{2}{9}\)b⁵

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

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

\( \frac{4 x 5}{2 x 5} \) - \( \frac{9 x 1}{10 x 1} \)

\( \frac{20}{10} \) - \( \frac{9}{10} \)

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

\( \frac{20 - 9}{10} \) = \( \frac{11}{10} \) = 1\(\frac{1}{10}\)

To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1 gallons so:

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

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46