Pleaseeeeee help. Picture attached

Question

asked Jan 11, 2022 214k views

1 Answer

Jonathan Irvin · Answer 1 · 2022-01-17T05:48:14+0000

Answer:

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.