Use the Properties of Exponents to Simplify the Expression $4 x ^ { - 2 / 5 } ( x -^ { 11 / 5 } - 5 x )$

question 17

Multiple Choice

Use the properties of exponents to simplify the expression. Write with positive exponents.
- $4 x ^ { - 2 / 5 } ( x -^ { 11 / 5 } - 5 x )$

• A) \(4 x ^ { 9 / 5 } + 5 x ^ { - 2 / 5 }\)
• B) \(\frac { 4 } { x ^ { 9 / 5 } } - \frac { 20 } { x ^ { - 2 / 5 } }\)
• C) \(4 x ^ { 9 / 5 } - 20 x ^ { 3 / 5 }\)
• D) \(4 x ^ { - 22 / 5 } - 20 x ^ { - 2 / 5 }\)

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Definitions:

Midpoint Method

A technique used in economics to calculate the elasticity of demand or supply, measuring the percentage change in quantity demanded or supplied relative to a percentage change in price.

Price Elasticity

A metric determining how the quantity of a good demanded fluctuates with a shift in that good's price.

Quantity Demanded

The total amount of goods or services that consumers are willing to buy at a given price over a certain period.

Inelastic

Describes a situation where the demand or supply for a good or service is relatively unaffected by changes in price.