Question

simplify. 81^{-\frac{1}{2}}

Explanation:

Step1: Recall negative - exponent rule

$a^{-n}=\frac{1}{a^{n}}$, so $81^{-\frac{1}{2}}=\frac{1}{81^{\frac{1}{2}}}$.

Step2: Recall square - root rule

$a^{\frac{1}{2}}=\sqrt{a}$, so $81^{\frac{1}{2}}=\sqrt{81}=9$.

Step3: Calculate the final result

Since $81^{\frac{1}{2}} = 9$, then $\frac{1}{81^{\frac{1}{2}}}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$