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

\( \frac{42\sqrt{4}}{6\sqrt{2}} \)
\( \frac{42}{6} \) \( \sqrt{\frac{4}{2}} \)
7 \( \sqrt{2} \)

The equation for this sequence is:

a_n = a_n-1 + 4(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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{9 x 3}{3 x 3} \) + \( \frac{4 x 1}{9 x 1} \)

\( \frac{27}{9} \) + \( \frac{4}{9} \)

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

\( \frac{27 + 4}{9} \) = \( \frac{31}{9} \) = 3\(\frac{4}{9}\)

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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