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:

-7c⁷ x 5c³
(-7 x 5)c^{(7 + 3)}
-35c¹⁰

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.

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.

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

\( \frac{9}{100} \) x 8 = \( \frac{9 \times 8}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour

So, in an average hour, the machine will produce 8 - 0.72 = 7.28 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 7.28 = 145.6 error free parts were produced yesterday.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,500
i = 0.02 x $1,500
i = $30