The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

The number of students taking German or Spanish is 15 + 8 = 23. Of that group of 23, 6 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 23 - 6 = 17 who are taking at least one language. 25 - 17 = 8 students who are not taking either language.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

If the tiger has consumed 130 pounds of food in 10 days that's \( \frac{130}{10} \) = 13 pounds of food per day. The tiger needs to consume 169 - 130 = 39 more pounds of food to reach 169 pounds total. At 13 pounds of food per day that's \( \frac{39}{13} \) = 3 more days.

The amount of flour you need is (3\(\frac{1}{2}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{28}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{27}{8} \) cups
3\(\frac{3}{8}\) cups