Express the Following Expression in Simplest Radical Form $$\frac { \sqrt [ 3 ] { 45 x y } } { \sqrt [ 3 ] { 5 x ^ { 2 } y ^ { 5 } } }$$

question 88

Multiple Choice

Express the following expression in simplest radical form. All variables represent positive real numbers. $$\frac { \sqrt [ 3 ] { 45 x y } } { \sqrt [ 3 ] { 5 x ^ { 2 } y ^ { 5 } } }$$

• A) \(\frac { 3 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }\)
• B) \(\frac { \sqrt [ 3 ] { 9 x y } } { y }\)
• C) \(\frac { 9 \sqrt [ 3 ] { x y } } { x y ^ { 2 } }\)
• D) \(\frac { \sqrt [ 3 ] { 9 x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }\)
• E) \(\frac { \sqrt [ 3 ] { 9 } } { x y ^ { 3 } }\)

---

Definitions:

Doublet

A pattern observed in NMR spectroscopy, indicating two adjacent hydrogen atoms influencing the resonance of another hydrogen or group.

Off-Resonance Decoupled

A technique in NMR spectroscopy where decoupling is applied at a frequency offset from the resonance frequency of the nucleus of interest to simplify spectra.

Multiplicities

In nuclear magnetic resonance (NMR) spectroscopy, multiplicities refer to the splitting pattern of a signal, indicating the number of nearby hydrogens (or other nuclei) interacting with the observed nucleus.

Molecular Formula

A representation of the actual number and type of atoms in a molecule, without indicating the structure or arrangement.