Final answer:
The simplified expression of (729x^3y^20z^11)1/5 is 3x3/5 y^4 z11/5.
Step-by-step explanation:
The expression provided by the student (729x^3y^20z^11)1/5 must be simplified by taking the fifth root of each component within the parentheses. When working with powers and roots, the rules of exponents indicate that each factor in the base—including numbers and variables with exponents—is affected by the root. Therefore, the fifth root of 729 is 3, since 729 is 3 to the power of 6 and 6/5 simplifies to 3 when reduced. Similarly, we apply the exponent of 1/5 to each variable exponent: x^3 becomes x3/5, y^20 becomes y^4, and z^11 becomes z11/5. Therefore, the simplified expression is 3x3/5 y4 z11/5.