A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{2}{3} \) = \( \frac{82000}{3} \) = 27,333 fans.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,500
i = 0.02 x $1,500
i = $30

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{64} \) = \( \frac{\frac{36}{4}}{\frac{64}{4}} \) = \( \frac{9}{16} \)

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:

\( \frac{-3x^7}{9x^4} \)
\( \frac{-3}{9} \) x^{(7 - 4)}
-\(\frac{1}{3}\)x³