Question

Pleaseeeeee help. Picture attached

Answer 1

Option C

Explanation:

Given expression is
`y^{-(4)/(3)}`.

Exponent of this expression is
`(-(4)/(3))`.

Option (A)

`-(4)/(3)y`

Since, exponents and coefficients of both the expressions are different.

They are not equivalent.

Option (B)

`-(\sqrt[3]{y})^4=-(y^{(1)/(3)})^4`

`=-y^{(4)/(3)}`

Here, exponent is with positive notation
`(+(4)/(3))` while in the original expression it is negative
`(-(4)/(3))`.

Therefore, both the expressions are not equivalent.

Option (C)

`\frac{1}{(\sqrt[3]{y})^4}=(\sqrt[3]{y})^(-4)`

`=y^{-(4)/(3)}`

Both the expressions are equivalent.

Option (D)

`-(\sqrt[4]{y})^3=-(y)^{(3)/(4)}`

Exponents of both the expressions are different.

Therefore, not equivalent.

Option (E)

`\frac{1}{(\sqrt[4]{x})^3}=(\sqrt[4]{x})^(-3)`

`=y^{-(3)/(4)}`

Exponent of this expression is different from the original expression.

Therefore, not equivalent.

Option (C) will be the correct option.