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

4\( \sqrt{6} \) x 5\( \sqrt{7} \)
(4 x 5)\( \sqrt{6 \times 7} \)
20\( \sqrt{42} \)

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:

\( \frac{8a^6}{5a^2} \)
\( \frac{8}{5} \) a^{(6 - 2)}
1\(\frac{3}{5}\)a⁴

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:

-1y³ + 3y³
(-1 + 3)y³
2y³

If the tiger has consumed 72 pounds of food in 8 days that's \( \frac{72}{8} \) = 9 pounds of food per day. The tiger needs to consume 99 - 72 = 27 more pounds of food to reach 99 pounds total. At 9 pounds of food per day that's \( \frac{27}{9} \) = 3 more days.

The number of students taking German or Spanish is 11 + 5 = 16. Of that group of 16, 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 16 - 3 = 13 who are taking at least one language. 27 - 13 = 14 students who are not taking either language.