Use the Binomial Theorem to Expand and Simplify the Expression $$\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$$

question 77

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression.
$$\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$$

• A) \(x ^ { 3 } + 625\)
• B) \(x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625\)
• C) \(x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625\)
• D) \(x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625\)
• E) \(x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625\)

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Definitions:

Marginal Product

The additional output that results from the use of one more unit of a variable input, assuming all other inputs remain constant, often reflecting the efficiency of the input.

Fringe Benefits

Additional benefits offered to employees on top of their salaries, such as health insurance, retirement plans, and paid vacation.

Labor Market

The supply and demand for labor, where employees provide the labor, and employers provide the jobs.

Equilibrium

A condition where the supply and demand in the market are equal, leading to stable prices.