Question

Which expression is equivalent to x y Superscript two-ninths?

Answer 1

Answer:

D. x (RootIndex 9 StartRoot y squared EndRoot)

Step-by-step explanation:

Edge 2020

Answer 2

Option D: $x\sqrt[9]{y^2}$ is the expression equivalent to $xy^{\frac{2}{9}}$

Explanation:

Option A: $\sqrt{xy^9}$

The expression can be written as $({xy^9})^{\frac{1}{2}$

Applying exponent rule, we get,

$x^{\frac{1}{2}} y^{\frac{9}{2}}$

Thus, the expression $\sqrt{xy^9}$ is not equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option A is not the correct answer.

Option B: $\sqrt[9]{xy^2}$

The expression can be written as $({xy^2})^{\frac{1}{9}$

Applying exponent rule, we get,

$x^{\frac{1}{9}} y^{\frac{2}{9}}$

Thus, the expression $\sqrt[9]{xy^2}$ is not equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option B is not the correct answer.

Option C: $x\sqrt{y^9}$

The expression can be written as $x(y^9)^{\frac{1}{2} }$

Applying exponent rule, we get,

$x y^{\frac{9}{2}}$

Thus, the expression $x\sqrt{y^9}$ is not equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option C is not the correct answer.

Option D: $x\sqrt[9]{y^{2} }$

The expression can be written as $x(y^2)^{\frac{1}{9} }$

Applying exponent rule, we get,

$xy^{\frac{2}{9}}$

Thus, the expression $xy^{\frac{2}{9}}$ is equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option D is the correct answer.