Question

Which expression is equivalent to 4square root 16x^11y^8/81x^7y^6

Answer 1

the answer would be
`(2x√(y))/(3)`

hope this helps! :)

Answer 2

`(2x√(y))/(3)`

Explanation:

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

LEts simplify the fraction inside the radical

we use rule of exponents to simplify the variables

`(a^m)/(a^n) =a^(m-n)`

When the exponents are in division with same base then we subtract the exponents

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

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

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

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

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

Equivalent expression is

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

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

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

`(2x√(y))/(3)`