To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

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

\( \frac{5 x 7}{5 x 7} \) - \( \frac{6 x 5}{7 x 5} \)

\( \frac{35}{35} \) - \( \frac{30}{35} \)

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

\( \frac{35 - 30}{35} \) = \( \frac{5}{35} \) = \(\frac{1}{7}\)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.78 = 94 points. Each question is worth 2 points so she got \( \frac{94}{2} \) = 47 questions right.

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

40,000 fans x \( \frac{3}{4} \) = \( \frac{120000}{4} \) = 30,000 fans.