Simplify the Expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$

question 3

Multiple Choice

Simplify the expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$ . Assume that neither u nor v is zero.

• A) \(\frac { 2 v ^ { 2 } } { 25 u ^ { 2 } }\)
• B) \(\frac { 2 v ^ { 2 } } { 25 }\)
• C) \(\frac { 2 v ^ { 4 } } { 5 u ^ { 2 } }\)
• D) \(\frac { 2 v } { 5 }\)
• E) \(\frac { 2 } { v ^ { 2 } }\)

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Definitions:

Average Product

This measures the productivity of inputs by dividing total production by the number of inputs, indicating the efficiency of input use.

Total Product

The total quantity of output produced by a firm or economy as a result of combining inputs of labor and capital over a specific time period.

Average Product

The output produced per unit of input used, calculated by dividing total output by the quantity of inputs.

Labor

The effort by humans to produce goods or services in the economy.