Simplify the Expression and Eliminate Any Negative Exponent(s) $\frac { \left( 64 y ^ { 6 } z ^ { - 12 } \right) ^ { - 1 / 6 } } { \left( 32 y ^ { - 5 } z ^ { 10 } \right) ^ { 1 / 5 } }$

question 48

Short Answer

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. $\frac { \left( 64 y ^ { 6 } z ^ { - 12 } \right) ^ { - 1 / 6 } } { \left( 32 y ^ { - 5 } z ^ { 10 } \right) ^ { 1 / 5 } }$

---

Definitions:

Control Group

In experimental research, a group of subjects not exposed to the treatment being studied, used as a baseline to measure the effect of the treatment.

Laboratory Experiment

A controlled study conducted in a specially equipped environment where variables can be manipulated and outcomes measured.

Field Experiment

A study conducted in a real-world setting where the researcher manipulates one or more variables to observe the effect on a particular outcome.

Independent Variable

The factor in an experiment that is intentionally changed to observe its effect on the dependent variable.