Question

Which expression is equivalent

Answer 1

Given expression is

$\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}$

Radical is fourth root

first we simplify the terms inside the radical

$\frac{x^{11}}{x^7}=x^4$

$\frac{y^(8)}{y^6}=y^2$

So the expression becomes

$\sqrt[4]{\frac{16x^4y^2}{81}}$

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