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

\( \frac{56\sqrt{24}}{8\sqrt{8}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{24}{8}} \)
7 \( \sqrt{3} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 have in common.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{3 x 4}{2 x 4} \) - \( \frac{7 x 1}{8 x 1} \)

\( \frac{12}{8} \) - \( \frac{7}{8} \)

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

\( \frac{12 - 7}{8} \) = \( \frac{5}{8} \) = \(\frac{5}{8}\)

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).