Question

Which expression is equivalent

Answer 1

Given expression is

`\sqrt[4]{(16x^(11)y^8)/(81x^7y^6)}`

Radical is fourth root

first we simplify the terms inside the radical

`(x^(11))/(x^7)=x^4`

`(y^(8))/(y^6)=y^2`

So the expression becomes

`\sqrt[4]{(16x^4y^2)/(81)}`

Now we take fourth root

`\sqrt[4]{16} = 2`

`\sqrt[4]{81} = 3`

`\sqrt[4]{x^4} = x`

We cannot simplify fourth root (y^2)

After simplification , expression becomes

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

Answer is option B