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

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

\( \frac{4}{5} \) x \( \frac{1}{6} \) = \( \frac{4 x 1}{5 x 6} \) = \( \frac{4}{30} \) = \(\frac{2}{15}\)

To subtract 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:

\( \frac{3 x 3}{3 x 3} \) - \( \frac{6 x 1}{9 x 1} \)

\( \frac{9}{9} \) - \( \frac{6}{9} \)

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

\( \frac{9 - 6}{9} \) = \( \frac{3}{9} \) = \(\frac{1}{3}\)

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{44} \) = \( \frac{\frac{40}{4}}{\frac{44}{4}} \) = \( \frac{10}{11} \)

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

2\( \sqrt{9} \) x 8\( \sqrt{6} \)
(2 x 8)\( \sqrt{9 \times 6} \)
16\( \sqrt{54} \)

Now we need to simplify the radical:

16\( \sqrt{54} \)
16\( \sqrt{6 \times 9} \)
16\( \sqrt{6 \times 3^2} \)
(16)(3)\( \sqrt{6} \)
48\( \sqrt{6} \)