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

Explanation:

Step1: Rewrite 64 as a power - of 2

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

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 $2^{6\times\frac{5}{6}} = 2^5$

Step4: Evaluate $2^5$

$2^5=2\times2\times2\times2\times2 = 32$

Answer:

32