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

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

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

9\( \sqrt{6} \) x 8\( \sqrt{8} \)
(9 x 8)\( \sqrt{6 \times 8} \)
72\( \sqrt{48} \)

Now we need to simplify the radical:

72\( \sqrt{48} \)
72\( \sqrt{3 \times 16} \)
72\( \sqrt{3 \times 4^2} \)
(72)(4)\( \sqrt{3} \)
288\( \sqrt{3} \)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

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:

\( \frac{35\sqrt{8}}{7\sqrt{2}} \)
\( \frac{35}{7} \) \( \sqrt{\frac{8}{2}} \)
5 \( \sqrt{4} \)