Question

Which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5

Answer 1

Option D.
`\sqrt[4]{(3x^(2))/(2y)}`

Explanation:

`\sqrt[4]{(24x^(6)y)/(128x^(4)y^(5))}`

`\sqrt[4]{((24)/(128))* ((x^(6))/(x^(4)))* ((y)/(y^(5)))}`

=
`\sqrt[4]{((3)/(16))* {(x)^(6-4)}*{(y)^(1-5)}}`

=
`\sqrt[4]{((3)/(16))* x^(2)y^(-4)}`

=
`\sqrt[4]{(3)/((2)^(4))* x* y^(-4)}`

=
`\sqrt[4]{(3* x^{2)* ((y^(-1))/(2))^(4)}}`

=
`(y^(-1))/(2)\sqrt[4]{3x^(2)}`

=
`\sqrt[4]{(3x^(2))/(2y)}`

Option D.
`\sqrt[4]{(3x^(2))/(2y)}` is the correct answer.