simplify.\n64^{-\frac{5}{6}}

Explanation:

Step1: Rewrite 64 as a power of 2

$64 = 2^6$. So the expression becomes $(2^6)^{-\frac{5}{6}}$.

Step2: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, we have $(2^6)^{-\frac{5}{6}}=2^{6\times(-\frac{5}{6})}$.

Step3: Calculate the exponent

$6\times(-\frac{5}{6})=- 5$. So the expression is $2^{-5}$.

Step4: Use the negative - exponent rule

The negative - exponent rule $a^{-n}=\frac{1}{a^n}$ gives $2^{-5}=\frac{1}{2^5}$.

Step5: Calculate $2^5$

$2^5 = 32$. So $\frac{1}{2^5}=\frac{1}{32}$.

Answer:

$\frac{1}{32}$