Which expression is equivalent to \sqrt[4]{\frac{16x^(11)y{8} }{81x^(7) y^(2) } }? Assume x > 0 and y\\eq 0.

Question

Which expression is equivalent to
`\sqrt[4]{\frac{16x^(11)y{8} }{81x^(7) y^(2) } }`? Assume x > 0 and y
`\\eq 0`.

Answer 1

xy \sqrt{4y} /3[/tex]

Explanation:

`\sqrt[4]{16x^(11-7) }y^(8-2) } /\sqrt[4]{81} \\\= \sqrt[4]{4^(2) x^(4) }y^(6) } /\sqrt[4]{3^(4) } \\\\= ({4^(2) x^(4) }y^(6) })^{(1)/(4) } /( {3^(4))^{(1)/(4) } \\=({4^{(1)/(2) } x }y^{(3)/(2) } })/3\\=xy  √(4y) /3`