Simplify the Expression Write the Answer Without Using Negative Exponents $\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }$

question 111

Multiple Choice

Simplify the expression. $$\frac { \left( 8 ^ { - 2 } z ^ { - 5 } y \right) ^ { - 1 } } { \left( 5 y ^ { 5 } z ^ { - 1 } \right) ^ { 3 } \left( 5 y z ^ { - 1 } \right) ^ { - 2 } }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

• A) \(\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }\)
• B) \(\frac { 5 y ^ { 14 } } { 64 z ^ { 6 } }\)
• C) \(\quad \frac { 64 z ^ { 14 } } { 5 y ^ { 6 } }\)
• D) \(\frac { 8 z ^ { 5 } } { 5 y ^ { 15 } }\)

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Definitions:

IR

A type of spectroscopy used to identify and study chemicals through their interactions with infrared light, revealing molecular vibrations.

Cyclohexanone

A six-membered cyclic ketone, important as a solvent and as a precursor to nylon and other synthetic polymers.

Cyclohexanol

A secondary alcohol that consists of a cyclohexane ring with a hydroxyl group (-OH) attached.

IR Spectra

The graphical representation of infrared light absorption by molecules, used to identify chemical bonds and functional groups in a substance.