Question

Which expressions in the picture are equivalent to (v^-1)^1/9? Choose all answers that apply:

Answer 1

All of them: A, B, and C

Explanation:

Answer 2

A, B, and C

Explanation:

Recall the exponent property
`(a^b)^c=a^{(b\cdot c)`.

Therefore,

`(v^(-1))^(1/9)=(v^(1/9))^-1=v^(-1/9)`

In addition, fraction exponents can be written as radicals such that:

`a^(b/c)=\sqrt[c]{a^b}`

Thus,
`(\sqrt[9]{v})^(-1)=(v^(1/9))^(-1)=(v^(-1))^(1/9)`.

Therefore, answer choices A, B, and C are correct.