Simplify the Radical Expression $\sqrt [ 5 ] { 243 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 22 } }$

question 72

Multiple Choice

Simplify the radical expression. Assume that all variables represent positive real numbers.
- $\sqrt [ 5 ] { 243 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 22 } }$

• A) \(3 y ^ { 3 } \sqrt [ 5 ] { 3 x ^ { 3 } y ^ { 2 } }\)
• B) \(3 y ^ { 4 } \sqrt [ 5 ] { x ^ { 3 } y ^ { 2 } }\)
• C) \(3 x y ^ { 4 } \sqrt [ 5 ] { 3 x y ^ { 2 } }\)
• D) \(3 x y ^ { 3 } \sqrt [ 5 ] { x ^ { 2 } y ^ { 2 } }\)

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Definitions:

X-linked Recessive

A mode of inheritance where a recessive gene on the X chromosome causes a condition or trait to be expressed primarily in males.

X Chromosome

One of the two sex chromosomes, the X chromosome plays a crucial role in determining genetic traits and can be found in both males (XY) and females (XX).

Autosomal

Relating to any chromosome that is not a sex chromosome; autosomes are numbered from 1 to 22 in humans.

Dizygotic Twins

Also known as fraternal twins, are siblings born at the same time who have developed from two different eggs fertilized by two different sperm, sharing about 50% of their DNA.