Simplify: $\sqrt [ 3 ] { - 54 x ^ { 11 } y ^ { 9 } }$
A) $- 3 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { 2 x ^ { 2 } }$
B) $- 3 x ^ { 3 } y ^ { 33 } \sqrt { 2 }$
C) $- 2 x y ^ { 3 } \sqrt { 9 x ^ { 11 } x ^ { 9 } }$
D) $2 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { 3 x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The cube root of $-54x^{11}y^{9}$ can be simplified by factoring out the cube roots that are perfect cubes. $-54$ can be factored into $-27 \times 2$, where $-27$ is a perfect cube ($-3^3$). $x^{11}$ can be factored into $x^9 \times x^2$, where $x^9$ is a perfect cube ($x^3$^3). $y^9$ is already a perfect cube ($y^3$^3). Thus, the simplified form is $-3x^3y^3\sqrt[3]{2x^2}$.

Simplify −54x11y93\sqrt [ 3 ] { - 54 x ^ { 11 } y ^ { 9 } }3−54x11y9​

Simplify $\sqrt [ 3 ] { - 54 x ^ { 11 } y ^ { 9 } }$