Question

select the correct location on the table.
select the expression that is equivalent to $12^{-\frac{4}{7}}$.
$sqrt7{12^4}$ $sqrt4{12^7}$
$-(sqrt7{12^4})$ $-(sqrt4{12^7})$
$\frac{1}{sqrt7{12^4}}$ $\frac{1}{sqrt4{12^7}}$
$-(\frac{1}{sqrt7{12^4}})$ $-(\frac{1}{sqrt4{12^7}})$

Explanation:

Step1: Apply negative exponent rule

Recall $a^{-n}=\frac{1}{a^n}$, so:
$12^{-\frac{4}{7}} = \frac{1}{12^{\frac{4}{7}}}$

Step2: Convert rational exponent to root

Recall $a^{\frac{m}{n}}=\sqrt[n]{a^m}$, so:
$\frac{1}{12^{\frac{4}{7}}} = \frac{1}{\sqrt[7]{12^4}}$

Answer:

$\frac{1}{\sqrt[7]{12^4}}$