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:

\( \sqrt{\frac{64}{36}} \)
\( \frac{\sqrt{64}}{\sqrt{36}} \)
\( \frac{\sqrt{8^2}}{\sqrt{6^2}} \)
\( \frac{8}{6} \)
1\(\frac{1}{3}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{2 x 5}{3 x 5} \) + \( \frac{5 x 3}{5 x 3} \)

\( \frac{10}{15} \) + \( \frac{15}{15} \)

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

\( \frac{10 + 15}{15} \) = \( \frac{25}{15} \) = 1\(\frac{2}{3}\)

The amount of flour you need is (3 - \(\frac{7}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{24}{8} \) - \( \frac{7}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups

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:

5z² x 5z⁷
(5 x 5)z^{(2 + 7)}
25z⁹

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

\( \frac{3}{9} \) ÷ \( \frac{1}{9} \) = \( \frac{3}{9} \) x \( \frac{9}{1} \)

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

\( \frac{3}{9} \) x \( \frac{9}{1} \) = \( \frac{3 x 9}{9 x 1} \) = \( \frac{27}{9} \) = 3