To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{9}} \)
\( \frac{\sqrt{49}}{\sqrt{9}} \)
\( \frac{\sqrt{7^2}}{\sqrt{3^2}} \)
\( \frac{7}{3} \)
2\(\frac{1}{3}\)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

\( \frac{4}{100} \) x 5 = \( \frac{4 \times 5}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour

So, in an average hour, the machine will produce 5 - 0.2 = 4.8 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 4.8 = 91.2 error free parts were produced yesterday.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)

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:

8z³ x 8z²
(8 x 8)z^{(3 + 2)}
64z⁵