Question

Please help answer quickly!

Answer 1

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

`Used:\\√(a\cdot b)=√(a)\cdot√(b)\\\\(a^n)/(a^m)=a^(n-m)\\\\\sqrt[n]{a^n}=a\\\\\sqrt{(a)/(b)}=(√(a))/(√(b))\\\\\sqrt[n]{a^m}=a^(m)/(n)`

But your answer is:

`...=(2)/(3)\cdot\sqrt[4]{x^4}\cdot\sqrt[4]{y^2}=\frac{2x\left(\sqrt[4]{y^2}\right)}{3}`

Answer 2

The fourth root of 16/81 is 2/3.

x^11/x^7 = x^4. The fourth root of x^4 is x.

y^8/y^6 = y^2 which remains inside the fourth root.

Answer: B.