Question

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

StartRoot x y Superscript 9 Baseline EndRoot
RootIndex 9 StartRoot x y squared EndRoot
x (StartRoot y Superscript 9 EndRoot)
x (RootIndex 9 StartRoot y squared EndRoot)

Answer 1

D for E2020.

Step-by-step explanation:

Answer 2

Option D:
`x\sqrt[9]{y^2}` is the expression equivalent to
`xy^{(2)/(9)}`

Step-by-step explanation:

Option A:
`√(xy^9)`

The expression can be written as
`({xy^9})^{(1)/(2)`

Applying exponent rule, we get,

`x^{(1)/(2)} y^{(9)/(2)}`

Thus, the expression
`√(xy^9)` is not equivalent to the expression
`xy^{(2)/(9)}`

Hence, Option A is not the correct answer.

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

The expression can be written as
`({xy^2})^{(1)/(9)`

Applying exponent rule, we get,

`x^{(1)/(9)} y^{(2)/(9)}`

Thus, the expression
`\sqrt[9]{xy^2}` is not equivalent to the expression
`xy^{(2)/(9)}`

Hence, Option B is not the correct answer.

Option C:
`x√(y^9)`

The expression can be written as
`x(y^9)^{(1)/(2) }`

Applying exponent rule, we get,

`x y^{(9)/(2)}`

Thus, the expression
`x√(y^9)` is not equivalent to the expression
`xy^{(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)^{(1)/(9) }`

Applying exponent rule, we get,

`xy^{(2)/(9)}`

Thus, the expression
`xy^{(2)/(9)}` is equivalent to the expression
`xy^{(2)/(9)}`

Hence, Option D is the correct answer.