To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{8} \) x \( \frac{4}{8} \) = \( \frac{1 x 4}{8 x 8} \) = \( \frac{4}{64} \) = \(\frac{1}{16}\)

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).

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

35,000 fans x \( \frac{4}{5} \) = \( \frac{140000}{5} \) = 28,000 fans.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (4 + 3) ÷ 3 x 4 - 3²
P: 5 + (7) ÷ 3 x 4 - 3²
E: 5 + 7 ÷ 3 x 4 - 9
MD: 5 + \( \frac{7}{3} \) x 4 - 9
MD: 5 + \( \frac{28}{3} \) - 9
AS: \( \frac{15}{3} \) + \( \frac{28}{3} \) - 9
AS: \( \frac{43}{3} \) - 9
AS: \( \frac{43 - 27}{3} \)
\( \frac{16}{3} \)
5\(\frac{1}{3}\)