Question

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

Answer 1

the answer would be $\frac{2x\sqrt{y}}{3}$

hope this helps! :)

Answer 2

Answer:

$\frac{2x\sqrt{y}}{3}$

Step-by-step explanation:

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

LEts simplify the fraction inside the radical

we use rule of exponents to simplify the variables

$\frac{a^m}{a^n} =a^{m-n}$

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

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

$\frac{y^{8}}{y^6} =y^{8-6}=y^2$

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

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

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

Equivalent expression is

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

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

$\sqrt[4]{y^2} =y^\frac{2}{4} =y^\frac{1}{2}$

$\frac{2x\sqrt{y}}{3}$