An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 4}{2 x 4} \) - \( \frac{9 x 1}{8 x 1} \)

\( \frac{32}{8} \) - \( \frac{9}{8} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{32 - 9}{8} \) = \( \frac{23}{8} \) = 2\(\frac{7}{8}\)

The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 36 have in common.

The number of students taking German or Spanish is 12 + 14 = 26. Of that group of 26, 8 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 26 - 8 = 18 who are taking at least one language. 27 - 18 = 9 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).