Simplify: $\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }$
A) $3 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { 3 x ^ { 2 } }$
B) none of these
C) $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 2 x ^ { 2 } }$
D) $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 3 x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The cube root of $81x^8y^{21}$ simplifies to $3x^2y^7\sqrt[3]{3x^2}$ because $81 = 3^4$, $x^8 = (x^2)^4$, and $y^{21} = (y^7)^3$. Breaking it down: $81$ simplifies to $3^3$ outside the cube root (since $3^4$ under a cube root leaves one 3 outside and one inside), $x^8$ simplifies to $x^2$ outside and $x^2$ inside (since $x^2$ raised to the 4th power under a cube root leaves $x^2$ outside and $x^2$ inside), and $y^{21}$ simplifies to $y^7$ outside (since $y^7$ raised to the 3rd power is perfectly cubed).

Simplify 81x8y213\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }381x8y21​

Simplify $\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }$