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

\( \frac{4}{8} \) x \( \frac{1}{7} \) = \( \frac{4 x 1}{8 x 7} \) = \( \frac{4}{56} \) = \(\frac{1}{14}\)

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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:

\( \frac{-7a^7}{a^2} \)
\( \frac{-7}{1} \) a^{(7 - 2)}
-7a⁵

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{2} \) x 6\( \sqrt{2} \)
(7 x 6)\( \sqrt{2 \times 2} \)
42\( \sqrt{4} \)

Now we need to simplify the radical:

42\( \sqrt{4} \)
42\( \sqrt{2^2} \)
(42)(2)
84