Question

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

Answer 1

Answer:

All of them: A, B, and C

Step-by-step explanation:

Answer 2

Answer:

A, B, and C

Step-by-step 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.