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:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

The number of students taking German or Spanish is 14 + 7 = 21. Of that group of 21, 3 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 21 - 3 = 18 who are taking at least one language. 26 - 18 = 8 students who are not taking either language.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{15 + 11 + 16 + 10}{4} \) = \( \frac{52}{4} \) = 13

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-7x⁶ - 9x⁶
(-7 - 9)x⁶
-16x⁶

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

2\( \sqrt{50} \) + 3\( \sqrt{2} \)
2\( \sqrt{25 \times 2} \) + 3\( \sqrt{2} \)
2\( \sqrt{5^2 \times 2} \) + 3\( \sqrt{2} \)
(2)(5)\( \sqrt{2} \) + 3\( \sqrt{2} \)
10\( \sqrt{2} \) + 3\( \sqrt{2} \)

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