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 exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

5c² x 2c⁴
(5 x 2)c^{(2 + 4)}
10c⁶

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 32 have in common.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{8}{100} \) x 8 = \( \frac{8 \times 8}{100} \) = \( \frac{64}{100} \) = 0.64 errors per hour

So, in an average hour, the machine will produce 8 - 0.64 = 7.36 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 7.36 = 139.8 error free parts were produced yesterday.