A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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

7\( \sqrt{4} \) x 4\( \sqrt{4} \)
(7 x 4)\( \sqrt{4 \times 4} \)
28\( \sqrt{16} \)

Now we need to simplify the radical:

28\( \sqrt{16} \)
28\( \sqrt{4^2} \)
(28)(4)
112

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0009582 in scientific notation is 9.582 x 10^-4

To add 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:

\( \frac{2 x 7}{5 x 7} \) + \( \frac{8 x 5}{7 x 5} \)

\( \frac{14}{35} \) + \( \frac{40}{35} \)

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

\( \frac{14 + 40}{35} \) = \( \frac{54}{35} \) = 1\(\frac{19}{35}\)

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

\( \frac{1}{5} \) ÷ \( \frac{2}{6} \) = \( \frac{1}{5} \) x \( \frac{6}{2} \)

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

\( \frac{1}{5} \) x \( \frac{6}{2} \) = \( \frac{1 x 6}{5 x 2} \) = \( \frac{6}{10} \) = \(\frac{3}{5}\)