Answer:
The answer to your question is: 3x[tex]\sqrt[5]{2x^{3}y^{3} }[/tex]
Step-by-step explanation:
= [tex]\sqrt[5]{486x^{8}y^{3} }[/tex]
= [tex]\sqrt[5]{486} \sqrt[5]{x^{8} } \sqrt[5]{y^{3} }[/tex]
Find the prime factors of 486
486 2
243 3
81 3
27 3
9 3
3 3
1
Then, 486 = (2)(3⁵)
and x⁸ = x³x⁵
So
= [tex]\sqrt[5]{(2)(3^{5}) } \sqrt[5]{x^{3}x^{5} } \sqrt[5]{y^{3} }[/tex]
= 3x[tex]\sqrt[5]{2x^{3}y^{3} }[/tex]
= 3x(2x³y³)[tex]^{1/5}[/tex] or = 3x(2[tex]^{1/5} x^{3/5} y^{3/5}[/tex]
