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:

\( \sqrt{\frac{36}{9}} \)
\( \frac{\sqrt{36}}{\sqrt{9}} \)
\( \frac{\sqrt{6^2}}{\sqrt{3^2}} \)
\( \frac{6}{3} \)
2

The greatest common factor (GCF) is the greatest factor that divides two integers.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-z^5}{9z^2} \)
\( \frac{-1}{9} \) z^{(5 - 2)}
-\(\frac{1}{9}\)z³

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.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{5 x 5}{8 x 5} \) - \( \frac{6 x 4}{10 x 4} \)

\( \frac{25}{40} \) - \( \frac{24}{40} \)

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

\( \frac{25 - 24}{40} \) = \( \frac{1}{40} \) = \(\frac{1}{40}\)