To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 30.9km + 15.9km
total distance = 47.3km

To subtract 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 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

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

\( \frac{4 x 7}{3 x 7} \) - \( \frac{8 x 3}{7 x 3} \)

\( \frac{28}{21} \) - \( \frac{24}{21} \)

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

\( \frac{28 - 24}{21} \) = \( \frac{4}{21} \) = \(\frac{4}{21}\)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{9} \) x 5\( \sqrt{9} \)
(9 x 5)\( \sqrt{9 \times 9} \)
45\( \sqrt{81} \)

Now we need to simplify the radical:

45\( \sqrt{81} \)
45\( \sqrt{9 \times 9} \)
45\( \sqrt{9 \times 3^2} \)
(45)(3)\( \sqrt{9} \)
135\( \sqrt{9} \)

The amount of flour you need is (3\(\frac{3}{8}\) - 1\(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{27}{8} \) - \( \frac{13}{8} \)) cups
\( \frac{14}{8} \) cups
1\(\frac{3}{4}\) cups