According to the product rule for exponents, when you multiply two terms with the same base, you add their exponents together. Therefore, x^5 * x^2 is equal to x^(5+2), which simplifies to x^7.

Converting the fractions to decimals: 3/5 = 0.6, 2/3 ≈ 0.667, 7/9 ≈ 0.778, 9/11 ≈ 0.818, 8/9 ≈ 0.889. Only option C sequences these numbers properly from smallest to largest.

An exponent of -1 indicates the reciprocal of the base number. Therefore, 5^-1 is the reciprocal of 5, which is 1/5.

When an exponential term is raised to a power, multiply the exponents. Here, multiplying 3 by 3 gives an exponent of 9, leaving us with 5^9.

You can add radicals just like like terms when the numbers inside the roots are identical. Adding an implicit 1*sqrt(2) to 3*sqrt(2) yields 4*sqrt(2).

Adding the sequence of decimals strictly results in 1366.35. Therefore, matching it to the available correct option provides the total sum.

By multiplying the exponents according to the power of a power rule, we calculate 4 * 2 = 8. The base stays the same, resulting in 10^8.

An exponent of 1/3 means calculating the cube root. Since 3 * 3 * 3 = 27, the cube root of 27 is 3.

First, add the two known numbers on the left: 726.34 + 888.12 = 1614.46. Setting up the equation: 1614.46 - x = 1001.88 allows for calculating x = 1614.46 - 1001.88, which leaves 612.58.

The expression 10^-3 translates to 1/(10^3). Since 10^3 equals 1000, the final simplified value is 1/1000 (or 0.001).