For this case we must simplify the following expression:
[tex]\sqrt [5] {224x ^ {11} * y ^ 8}[/tex]
We follow the steps below:
We rewrite 224 as the product of: 32 * 7
[tex]\sqrt [5] {32 * 7 * x ^ {11} * y ^ 8} =[/tex]
We rewrite [tex]32\ as\ 2 ^ 5, x^{11}\ as\ x * x^{10}:[/tex]
[tex]\sqrt [5] {2 ^ 5 * 7 * x ^ {10} * x * y ^ 8} =[/tex]
We rewrite [tex]x^{10}[/tex] as [tex](x ^ 2) ^ 5,[/tex] we also rewrite [tex]y ^ 8[/tex] as [tex]y ^ 5 * y ^ 3:[/tex]
[tex]\sqrt [5] {2 ^ 5 * 7 * (x ^ 2) ^ 5 * x * y ^ 5 * y ^ 3} =[/tex]
We reorder:
[tex]\sqrt [5] {2 ^ 5 * (x ^ 2) ^ 5 * y ^ 5 * 7 * x * y ^ 3} =\\\sqrt [5] {(2 * x ^ 2 * y) ^ 5 * (7 * x * y ^ 3)} =[/tex]
We take the terms of the radical considering that: [tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
[tex]2 x ^ 2y \sqrt [5] {7 x y ^ 3}[/tex]
Answer:
Option A
