Question

Which expression is equivalent to

Answer 1

`\frac{\sqrt[4]{3x^2} }{2y}`

Explanation:

We can simplify the expression under the root first.

Remember to use
`(a^x)/(a^y)=a^(x-y)`

Thus, we have:

`\sqrt[4]{(24x^(6)y)/(128x^(4)y^(5))} \\=\sqrt[4]{(3x^(2))/(16y^(4))}`

We know 4th root can be written as "to the power 1/4th". Then we can use the property
`(ab)^(x)=a^x b^x`

So we have:

`\sqrt[4]{(3x^(2))/(16y^(4))} \\=((3x^(2))/(16y^(4)))^{(1)/(4)}\\=\frac{3^{(1)/(4)}x^{(1)/(2)}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}`

Option D is right.