To divide one fraction by another, you must multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, the calculation becomes $\frac{5}{8} \times \frac{4}{3}$. Multiplying the numerators ($5 \times 4 = 20$) and the denominators ($8 \times 3 = 24$) gives $\frac{20}{24}$. This fraction can be simplified by finding the greatest common divisor of 20 and 24, which is 4. Dividing the numerator and denominator by 4 ($20 \div 4 = 5$ and $24 \div 4 = 6$) gives the final simplified answer of $\frac{5}{6}$.

Combining the whole numbers and fractional parts: 555.05 + 55.50 + 5.55 + 5.00 + 0.55 leads mathematically to a total value of 621.65.

The second term has an implicit coefficient of 1. Subtracting 1 from 7 gives 6. The radical part remains the same, producing 6*sqrt(7).

Since the bases are the same, we simply subtract the exponents. Subtracting 3 from 9 leaves an exponent of 6, making the simplified form 4^6.

Simplify both terms first: sqrt(18) = 3*sqrt(2) and sqrt(8) = 2*sqrt(2). Subtracting them gives 3*sqrt(2) - 2*sqrt(2) = 1*sqrt(2), which is just sqrt(2).

The cube root of 343 is a number that, when raised to the third power, yields 343. That number is 7, because 7^3 = 343.

According to the quotient rule for exponents, we subtract the bottom exponent from the top exponent when bases are the same. Subtracting 4 from 9 gives us x^5.

Converting the given fractions reveals their order: 11/14 ≈ 0.786, 16/19 ≈ 0.842, and 19/21 ≈ 0.905. Therefore, the list progressing from lowest to highest is 11/14, 16/19, 19/21.

A variable without a visible exponent has an implicit exponent of 1. So, y^6 * y^1 means we add the exponents 6 and 1 together, resulting in y^7.

Adding up the digits yields 496.88 when properly lining up the numerical values relative to the decimal.