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:

\( \frac{3!}{2!} \)
\( \frac{3 \times 2 \times 1}{2 \times 1} \)
\( \frac{3}{1} \)
3

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:

\( \frac{-7x^5}{2x^3} \)
\( \frac{-7}{2} \) x^{(5 - 3)}
-3\(\frac{1}{2}\)x²

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 have in common.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{49}} \)
\( \frac{\sqrt{81}}{\sqrt{49}} \)
\( \frac{\sqrt{9^2}}{\sqrt{7^2}} \)
\( \frac{9}{7} \)
1\(\frac{2}{7}\)

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

\( \frac{3}{5} \) x \( \frac{2}{8} \) = \( \frac{3 x 2}{5 x 8} \) = \( \frac{6}{40} \) = \(\frac{3}{20}\)