Simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 4 ] { x ^ { 27 } }$
A) $x ^ { 6 } \sqrt { 3 }$
B) $x ^ { 4 } \sqrt [ 6 ] { x ^ { 3 } }$
C) $x \sqrt [ 4 ] { x ^ { 3 } }$
D) $x ^ { 4 } \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The expression $\sqrt [ 4 ] { x ^ { 27 } }$ simplifies to $x^{27/4}$, which can be further simplified to $x^{6}\cdot x^{3/4}$ or $x^6 \cdot \sqrt[4]{x^3}$. However, none of the options exactly match this form, indicating a mistake in my initial explanation. Correctly, it simplifies to $x^{27/4} = x^{6 + 3/4} = x^6 \cdot x^{3/4}$, which is closest to option C, $x \cdot \sqrt[4]{x^3}$, when considering the proper simplification of the exponent as $x^{(6\cdot4 + 3)/4} = x^{(24+3)/4} = x^{27/4}$. This indicates a need to correct the interpretation of how the exponent is simplified and matched with the given options. The correct simplification should directly consider the division of the exponent by 4, leading to $x^{6 + 3/4}$, which directly matches none of the options perfectly but intends to suggest the process of breaking down the exponent into a whole number and a fractional part for simplification.

Simplify Assume That All Variables Represent Positive Real Numbers x274\sqrt [ 4 ] { x ^ { 27 } }4x27​

Simplify Assume That All Variables Represent Positive Real Numbers $\sqrt [ 4 ] { x ^ { 27 } }$