The number of students taking German or Spanish is 9 + 6 = 15. Of that group of 15, 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 15 - 5 = 10 who are taking at least one language. 15 - 10 = 5 students who are not taking either language.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{25}} \)
\( \frac{\sqrt{4}}{\sqrt{25}} \)
\( \frac{\sqrt{2^2}}{\sqrt{5^2}} \)
\(\frac{2}{5}\)

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-3x⁴ x 9x⁷
(-3 x 9)x^{(4 + 7)}
-27x¹¹