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:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{4 x 3}{8 x 3} \) + \( \frac{3 x 2}{12 x 2} \)

\( \frac{12}{24} \) + \( \frac{6}{24} \)

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

\( \frac{12 + 6}{24} \) = \( \frac{18}{24} \) = \(\frac{3}{4}\)

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

2a² x a⁴
(2 x 1)a^{(2 + 4)}
2a⁶

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

\( \frac{20\sqrt{12}}{4\sqrt{4}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{12}{4}} \)
5 \( \sqrt{3} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: