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:

-9y² x 5y⁷
(-9 x 5)y^{(2 + 7)}
-45y⁹

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{5} \) ÷ \( \frac{3}{6} \) = \( \frac{2}{5} \) x \( \frac{6}{3} \)

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

\( \frac{2}{5} \) x \( \frac{6}{3} \) = \( \frac{2 x 6}{5 x 3} \) = \( \frac{12}{15} \) = \(\frac{4}{5}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 45mph \times 1h \)
45 miles

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 $1,400
i = 0.03 x $1,400
i = $42

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{7 x 5}{6 x 5} \) - \( \frac{3 x 3}{10 x 3} \)

\( \frac{35}{30} \) - \( \frac{9}{30} \)

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

\( \frac{35 - 9}{30} \) = \( \frac{26}{30} \) = \(\frac{13}{15}\)