Simplify the Expression $$- \sqrt { \frac { 27 x ^ { 3 } } { y 5 } }$$

question 492

Multiple Choice

Simplify the expression. Assume all variables represent positive real numbers.
- $$- \sqrt { \frac { 27 x ^ { 3 } } { y 5 } }$$

• A) \(- \frac { 3 x ^ { 3 } \sqrt { 3 } } { y ^ { 5 } }\)
• B) \(- \frac { 3 x } { y ^ { 2 } } \sqrt { \frac { 3 x } { y } }\)
• C) \(- \frac { 3 x \sqrt { 3 x y } } { y ^ { 3 } }\)
• D) \(- \frac { x \sqrt { 27 x y } } { y ^ { 3 } }\)

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Definitions:

Excludable

A characteristic of a good or service that means it can be prevented from being used by people who have not paid for it.

Private Goods

Goods that are excludable and rivalrous, meaning one person's consumption prevents another's and consuming the good diminishes its availability for others.

Common Resources

Resources that are accessible to all members of a community but are susceptible to overuse and depletion, such as air, water, and fish in the ocean.

Public Goods

Goods that are non-excludable and non-rivalrous, meaning their use by one person does not reduce availability to others, often provided by the government.