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

\( \frac{3}{6} \) ÷ \( \frac{2}{7} \) = \( \frac{3}{6} \) x \( \frac{7}{2} \)

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

\( \frac{3}{6} \) x \( \frac{7}{2} \) = \( \frac{3 x 7}{6 x 2} \) = \( \frac{21}{12} \) = 1\(\frac{3}{4}\)

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:

\( \frac{2 x 5}{6 x 5} \) - \( \frac{7 x 3}{10 x 3} \)

\( \frac{10}{30} \) - \( \frac{21}{30} \)

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

\( \frac{10 - 21}{30} \) = \( \frac{-11}{30} \) = -\(\frac{11}{30}\)

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:

-5a² x 3a³
(-5 x 3)a^{(2 + 3)}
-15a⁵

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

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:

\( \frac{9a^9}{5a^3} \)
\( \frac{9}{5} \) a^{(9 - 3)}
1\(\frac{4}{5}\)a⁶