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:

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

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{7} \) ÷ \( \frac{3}{7} \) = \( \frac{1}{7} \) x \( \frac{7}{3} \)

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

\( \frac{1}{7} \) x \( \frac{7}{3} \) = \( \frac{1 x 7}{7 x 3} \) = \( \frac{7}{21} \) = \(\frac{1}{3}\)

To add these radicals together their radicands must be the same:

5\( \sqrt{75} \) + 2\( \sqrt{3} \)
5\( \sqrt{25 \times 3} \) + 2\( \sqrt{3} \)
5\( \sqrt{5^2 \times 3} \) + 2\( \sqrt{3} \)
(5)(5)\( \sqrt{3} \) + 2\( \sqrt{3} \)
25\( \sqrt{3} \) + 2\( \sqrt{3} \)

Now that the radicands are identical, you can add them together: