Question

Pleaseeeeee help. Picture attached

Answer 1

Answer:

Option C

Step-by-step explanation:

Given expression is $y^{-\frac{4}{3}}$.

Exponent of this expression is $(-\frac{4}{3})$.

Option (A)

$-\frac{4}{3}y$

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

They are not equivalent.

Option (B)

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

            $=-y^{\frac{4}{3}}$

Here, exponent is with positive notation $(+\frac{4}{3})$ while in the original expression it is negative $(-\frac{4}{3})$.

Therefore, both the expressions are not equivalent.

Option (C)

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

         $=y^{-\frac{4}{3}}$

Both the expressions are equivalent.

Option (D)

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

Exponents of both the expressions are different.

Therefore, not equivalent.

Option (E)

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

         $=y^{-\frac{3}{4}}$

Exponent of this expression is different from the original expression.

Therefore, not equivalent.

Option (C) will be the correct option.