Begin by evaluating the left side: 832.58 - 242.31 = 590.27. Then arrange the right side calculation: x = 779.84 - 590.27 to pinpoint the correct missing value as 400.70.

Factor 20 into a perfect square and another number, which is 4 * 5. Taking the square root of 4 gives 2, which leaves us with the simplified form 2*sqrt(5).

For negative numbers, a larger absolute magnitude equates to a smaller value. Evaluating them: -7/10 = -0.700, -2/3 ≈ -0.667, -5/8 = -0.625. Ordering these from smallest to largest yields -7/10, -2/3, -5/8.

Raising to the power of 1/3 means finding the cube root. The cube root of 125 is 5, since 5 cubed (5 * 5 * 5) is equal to 125.

By applying the fundamental rule of exponents for multiplication, we add the exponents 2 and 3. The base remains 4, which gives us 4^5.

When multiplying powers of 10, the base remains 10 and the exponents are summed. The sum of 3 and 4 is 7, making the final expression 10^7.

The number 54 can be divided by the perfect cube 27 (27 * 2 = 54). Evaluating the cube root of 27 gives 3, so the expression simplifies to 3*cbrt(2).

When a term with an exponent is raised to an additional power, the exponents are multiplied. Multiplying 3 by 5 yields 15, making the simplified term z^15.

A negative exponent flips the position of the term in a fraction. Changing y^-4 to a positive exponent moves it to the denominator, becoming 1/y^4.

First, add the exponents: 3 + (-5) = -2, giving x^-2. Then, convert the negative exponent to a positive one by rewriting it as 1/x^2.