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

3\( \sqrt{3} \) x 8\( \sqrt{2} \)
(3 x 8)\( \sqrt{3 \times 2} \)
24\( \sqrt{6} \)

The number of students taking German or Spanish is 5 + 11 = 16. Of that group of 16, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 2 = 14 who are taking at least one language. 29 - 14 = 15 students who are not taking either language.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

6,591,000 in scientific notation is 6.591 x 10⁶

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.