For this case we must simplify the following expression:
[tex]\sqrt [3] {8x ^ 5 * y ^ 6}[/tex]
We know that:
[tex]8 = 2 ^ 3[/tex]
[tex]x ^ 5 = x ^ 3 * x ^ 2[/tex](To multiply powers of the same base, place the same base and add the exponents)
In addition, by definition of power properties we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Rewriting the expression we have:
[tex]\sqrt [3] {2 ^ 3 * x ^ 3 * x ^ 2 * y ^ 6} =[/tex]
Applying the mentioned property we have:
[tex]2 ^ {\frac {3} {3}} * x ^ {\frac {3} {3}} * y ^ {\frac {6} {3}} \sqrt [3] {x ^ 2} =\\2xy ^ 2 \sqrt [3] {x ^ 2}[/tex]
Answer:
[tex]2xy ^ 2 \sqrt [3] {x ^ 2}[/tex]
