First perform the left side calculations: 534.596 + 61.472 = 596.068. Then subtract 496.708 to get 99.36. Subtracting 27.271 from 99.36 yields 72.089.

By applying the quotient rule for exponents, we subtract the bottom exponent (5) from the top exponent (12). This operation yields z^7.

Express 27 as a power of 3, which is 3^3. Setting the exponents equal from the equation 3^x = 3^3 tells us that x equals 3.

An exponent of 1/5 asks for the fifth root of the number. The fifth root of 32 is 2, because multiplying 2 by itself five times yields 32.

Evaluating the square root of a perfect square like 49 requires finding the number that multiplies by itself to get 49, which is exactly 7.

Square both sides to eliminate the radical, creating the equation x - 2 = 16. Then, add 2 to both sides to solve for x, resulting in x = 18.

Dividing the numerator (1999) by the denominator (2111) gives a value of approximately 0.9469... Rounding to three decimal places results in 0.946.

The target threshold is 1/5, which equals 0.200. Calculating the decimal forms: 8/35 ≈ 0.229, 8/37 ≈ 0.216, 8/39 ≈ 0.205, and 2/11 ≈ 0.182. Only 2/11 produces a value smaller than 0.200.

Since the radicands (number under the root) are the same, treat sqrt(5) as a variable. Add the coefficients 2 and 4 to get 6, giving a result of 6*sqrt(5).

The quotient rule dictates subtracting the denominator's exponent from the numerator's. Performing 5 - 2 yields 3, giving a final simplified expression of 10^3.