Converting to decimals to compare values: 13/16 = 0.8125, 15/19 ≈ 0.7895, 17/21 ≈ 0.8095, 7/8 = 0.875. The lowest value among these choices is 15/19.

When multiplying square roots, multiply the numbers inside the radicals together. This gives sqrt(36), and since 36 is a perfect square, the square root is 6.

Write 125 with a base of 5. Because 5 * 5 * 5 = 125, we know 125 is 5^3. Equating the exponents from 5^x = 5^3 gives x = 3.

Subtracting the exponents gives 8^(4-4) = 8^0. Any non-zero base raised to the power of zero equals 1. Alternatively, any number divided by itself is 1.

One centimetre is equal to 1/100,000 kilometres. Consequently, one hundredth of a centimetre equates to 1/100 * 1/100,000 km, leading to a direct value of 0.0000001 kilometers.

First, divide both sides by 2 to isolate the radical, giving sqrt(x) = 5. Next, square both sides to find x. Squaring 5 results in x = 25.

First, sum the negative amounts: 53.74 + 62.86 = 116.60. Next, execute the final subtraction: 341.42 - 116.60 = 224.82.

Finding the square root of 121 means identifying what positive number squared gives 121. The answer is 11, because 11 * 11 = 121.

The product rule tells us to add the exponents when the base is identical. Adding the exponent 1 to the exponent 6 gives a final power of 7, so the answer is 7^7.

To convert the fraction to a decimal, divide 10127 by 100000. This is done by shifting the decimal point five places to the left, which results in 0.10127.