Question

simplify.
81$^{-\frac{1}{4}}$

Explanation:

Step1: Rewrite 81 as a power.

$81 = 3^4$, so $81^{-\frac{1}{4}}=(3^4)^{-\frac{1}{4}}$

Step2: Apply power - of - a - power rule.

According to $(a^m)^n=a^{mn}$, we have $(3^4)^{-\frac{1}{4}}=3^{4\times(-\frac{1}{4})}$

Step3: Calculate the exponent.

$4\times(-\frac{1}{4})=- 1$, so $3^{4\times(-\frac{1}{4})}=3^{-1}$

Step4: Use negative - exponent rule.

$a^{-n}=\frac{1}{a^n}$, so $3^{-1}=\frac{1}{3}$

Answer:

$\frac{1}{3}$