Use the Rules of Exponents to Simplify the Expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$

question 35

Multiple Choice

Use the rules of exponents to simplify the expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$ using only positive exponents. Assume that no variable is zero.

• A) \(\frac { 64 y ^ { 30 } } { x ^ { 30 } }\)
• B)1
• C) \(\frac { 64 x ^ { 30 } } { y ^ { 30 } }\)
• D) \(\frac { - 4 y ^ { 30 } } { x ^ { 30 } }\)
• E) 64

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Definitions:

Standard Error of Estimate

A statistical measure that provides an estimation of the standard deviation of the error term in a regression model, indicating the accuracy of predictions.

Coefficient of Determination

A measure in statistical models that indicates the proportion of the variance in the dependent variable predictable from the independent variables, often symbolized as \(R^2\).

Multicollinearity

A statistical phenomenon in which predictor variables in a regression model are highly correlated, potentially leading to difficulties in estimating separate effects on the dependent variable.

Dependent Variable

A variable in an experiment or model whose value is affected by changes in other (independent) variables.