which of the following is equivalent to $36^{-\frac{1}{2}}$?\n-18\n-6\n$\frac{1}{18}$\n$\frac{1}{6}$

Answer:

D. $\frac{1}{6}$

Explanation:

Step1: Use negative - exponent rule

$a^{-n}=\frac{1}{a^{n}}$, so $36^{-\frac{1}{2}}=\frac{1}{36^{\frac{1}{2}}}$.

Step2: Use fractional - exponent rule

$a^{\frac{1}{n}}=\sqrt[n]{a}$, then $36^{\frac{1}{2}}=\sqrt{36} = 6$.

Step3: Get the final result

$\frac{1}{36^{\frac{1}{2}}}=\frac{1}{6}$.