Question

select the correct location on the table. select the expression that is equivalent to 12^(-4/7).

Explanation:

Step1: Use negative - exponent rule

By the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$, for the expression $12^{-\frac{4}{7}}$, we have $12^{-\frac{4}{7}}=\frac{1}{12^{\frac{4}{7}}}$.

Step2: Use fractional - exponent rule

The fractional - exponent rule states that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $12^{\frac{4}{7}}=\sqrt[7]{12^{4}}$. Then $\frac{1}{12^{\frac{4}{7}}}=\frac{1}{\sqrt[7]{12^{4}}}$.

Answer:

$\frac{1}{\sqrt[7]{12^{4}}}$ (corresponding to the bottom - left cell in the table where the expression is $\frac{1}{\sqrt[7]{12^{4}}}$)