Simplify the Following Algebraic Expression and Express Your Answer Using $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$

question 171

Multiple Choice

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$

• A) \(\frac { 1 } { 243 x ^ { 11 } y ^ { 35 } }\)
• B) \(\frac { 8 } { x ^ { 30 } y ^ { 12 } }\)
• C) \(\frac { 243 } { x ^ { 11 } y ^ { 12 } }\)
• D) \(\frac { 3 } { 243 x ^ { 30 } y ^ { 35 } }\)
• E) \(\frac { 1 } { 243 x ^ { 30 } y ^ { 35 } }\)

---

Definitions:

Symbiotic Relationship

A close and often long-term interaction between two different biological species, where both species benefit from the relationship.

Etiology

The study of causation, or origination; used particularly in the context of disease to determine its cause.

Normative Ethics

A branch of ethics concerned with the criteria of what is morally right and wrong, focusing on the establishment of moral standards that regulate right and wrong conduct.

Proper Behavior

Conduct that is deemed appropriate, respectful, and considerate according to societal norms and expectations.