Question

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

Explanation:

Step1: Rewrite 64 as a power

$64 = 2^6$, so $64^{-\frac{5}{6}}=(2^6)^{-\frac{5}{6}}$

Step2: Apply power - of - a - power rule

$(a^m)^n=a^{mn}$, then $(2^6)^{-\frac{5}{6}}=2^{6\times(-\frac{5}{6})}$

Step3: Calculate the exponent

$6\times(-\frac{5}{6})=- 5$, so $2^{6\times(-\frac{5}{6})}=2^{-5}$

Step4: Use negative - exponent rule

$a^{-n}=\frac{1}{a^n}$, then $2^{-5}=\frac{1}{2^5}$

Step5: Calculate $2^5$

$2^5 = 32$, so $\frac{1}{2^5}=\frac{1}{32}$

Answer:

$\frac{1}{32}$