The number of students taking German or Spanish is 7 + 10 = 17. Of that group of 17, 5 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 17 - 5 = 12 who are taking at least one language. 22 - 12 = 10 students who are not taking either language.

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

4\( \sqrt{80} \) - 7\( \sqrt{5} \)
4\( \sqrt{16 \times 5} \) - 7\( \sqrt{5} \)
4\( \sqrt{4^2 \times 5} \) - 7\( \sqrt{5} \)
(4)(4)\( \sqrt{5} \) - 7\( \sqrt{5} \)
16\( \sqrt{5} \) - 7\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

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:

\( \frac{-6b^9}{b^3} \)
\( \frac{-6}{1} \) b^{(9 - 3)}
-6b⁶

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

2c³ + 2c³
(2 + 2)c³
4c³

The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 20 are [1, 2, 4, 5, 10, 20]. They share 3 factors [1, 2, 4] making 4 the greatest factor 76 and 20 have in common.