Answer:
Option C
Step-by-step explanation:
Given expression is [tex]y^{-\frac{4}{3}}[/tex].
Exponent of this expression is [tex](-\frac{4}{3})[/tex].
Option (A)
[tex]-\frac{4}{3}y[/tex]
Since, exponents and coefficients of both the expressions are different.
They are not equivalent.
Option (B)
[tex]-(\sqrt[3]{y})^4=-(y^{\frac{1}{3}})^4[/tex]
[tex]=-y^{\frac{4}{3}}[/tex]
Here, exponent is with positive notation [tex](+\frac{4}{3})[/tex] while in the original expression it is negative [tex](-\frac{4}{3})[/tex].
Therefore, both the expressions are not equivalent.
Option (C)
[tex]\frac{1}{(\sqrt[3]{y})^4}=(\sqrt[3]{y})^{-4}[/tex]
[tex]=y^{-\frac{4}{3}}[/tex]
Both the expressions are equivalent.
Option (D)
[tex]-(\sqrt[4]{y})^3=-(y)^{\frac{3}{4}}[/tex]
Exponents of both the expressions are different.
Therefore, not equivalent.
Option (E)
[tex]\frac{1}{(\sqrt[4]{x})^3}=(\sqrt[4]{x})^{-3}[/tex]
[tex]=y^{-\frac{3}{4}}[/tex]
Exponent of this expression is different from the original expression.
Therefore, not equivalent.
Option (C) will be the correct option.
